how are you guys welcome to today's class super excited to have all of you guys here with me we're gonna be focusing on men's cutting today it's Monday that's what we do if you're new to the show if you've never watched one of my live streams before welcome type new in the chat let me know that and also if you're an og been watching this for a long time you guys are what hold this whole thing together so make sure type og in the chat let us know where you're from also a couple other things let's see what else do we need to do um so let us know where you're from make sure you share the show let's get this room as big as possible and also know that we are live on the nerve of beauty comms Facebook as well so shout out to them they've been sponsoring this show since the beginning since quarantine started a long time ago and you know we're still rolling through it having a lot of fun being live teaching you guys pretty much every single day so I'm excited to be a part of this and look at all these people in the chat you guys are awesome thank you so much again just hit the share button let's grow this room as much as possible and that's pretty much it let me break down what we're gonna do the other thing I want to do is make sure that I have this shut off there we go alright so those of you guys that are new to the show you know this is kind of all about doing a haircut filming it for YouTube and allowing you guys to be live with me to watch me do it ask questions so I want you guys to get involved as much as possible if you have a question type Q put that in the question so just type Q then write your question that way I can see it and we can go from there alright cool the room is growing guys you're doing a wonderful job just keep sharing it alright let's break down what we're gonna do with the haircut we go here record alright so like I said we're gonna be working on a men's haircut today I want to really focus on a faux-hawk now not that a faux-hawk is super trendy right now but I think pretty much any haircut that goes with a person is a trendy haircut I also want to show you guys it's not it doesn't have to be it can be very versatile doesn't have to be a faux-hawk but what I want to do is show you guys how to kind of get that gravity point of the haircut to the center or where most of the weight is falling to or pushing to so we're gonna go right there into the center and then I'm also gonna bring it a little bit back into the crown area and I'm gonna pop some weight and movement into the back as well so that's kind of the goal with this cut today we're gonna do a little bit of clippering a little bit of scissoring a little bit of tri-raiser we're gonna have you know every little aspect in there as we work through it. Kel what's up good to see you Marsha thank you so much I appreciate the the nice words Elaine good to see you Kel again Jess Mac Shirley Sophie Karen you guys are all awesome Sue good to see you oh gee in Michigan nice nice Lawrence or Laurence hello good to see you and then we got Kate Harris tell it's a cool name tell so listen I really appreciate you guys you know it's it's it's kind of crazy like being live on here all the time and I really appreciate that those of you that take the time out of your day to watch these streams share them you know and be a part of it so thank you guys Kristen good to see you Pittsburgh PA awesome other side of the state we're near Philadelphia Shelly good to see you thank you hope good to see you as well Jessica Zina very cool I love seeing everybody and where you guys are from sup bro Jay Caesar good to see you Tina in Illinois that's where I'm from good to see you Giselle Jess Mac says breathe I can't breathe oh so here's the thing so I'm tons of energy today feeling feeling really good and excited there's a lot of new things going on with free salon education so one thing I want to share with you guys before I get started is the new app update so if you guys haven't updated your FSE now app I really suggest that you do I think we're on version let me see exactly what it is so if you go to the app store you type in FSE free salon education FSE now then you'll see it right here and it's version 1.6 so that's what you want to be on it just came out today the cool thing about this is that now you can go live if you want to as a stylist so you can talk to people on there you can share anything you can ask questions so let's say I have a question about a client I can go live and I can ask a world of hairdressers live on there they'll chat some answers back to you and it's really all about building this community even bigger I can also go live talk to you guys teach you guys different things so we're gonna do some exclusive stuff on here also the virtual cutting club that has been a club that's been meeting every Monday over zoom which used to be a paid club has not been a paid club now for about a month and I'm now inviting people if you download the app you will get invites to come join us on zoom cut hair with me live I can watch you cut hair it's a really really fun thing and the people within that group we become you know close friends I would say I know them really well I know how they cut hair I watch them cut hair all the time I love for you to be a part of that group as well let's see we can go live and have a chat that's exactly it Jess so you can go live just make sure that you follow each other because then that's how you get the alerts so you go on to the app you go to the community so just like this click little people button here that'll put you in the community and then anybody that you see so like Jamie right here so if I tap Jamie's name I can follow Jamie just like that once I'm following Jamie if Jamie goes live I get an alert on the app I can go join her in a live room and listen to what she has to say so super cool really excited for it also another little update is that you can now share video links so you tap video link you paste in whatever YouTube video inspired you so whether it's a free salon education video Sam via video Paul Mitchell video whatever it is find it on YouTube paste the link in there talk about it post it to the community we'd love to have you guys sharing education videos that inspire you as well and then of course your pictures so under image you just click the image you can edit your photos within this app and then post them on to the community which then posts your work on stylist locator so that clients can go find you by using their zip code so if you're a client out there and you're watching this video for inspiration go to stylist locator.com put in your zip code and they'll pull up everybody that's a part of our FSE now community and you'll be able to see their work see if they're the right fit for you send them a message get booked into the salon it's a full circle community thing that we have going on all right and Smo Mo I see that you're on here I got your email and I'm gonna be writing you back as soon as this live stream is over just been trying to find the moment to do it but we'll get you going in the app as well all right Kristen good to see you Elena good to see you I'm gonna talk stop talking now I would love to join your live cutting class problem as I work on Mondays it's totally cool you can watch the replays that's the other thing look for the VCC replays on the app and you can watch them later all right those of you guys that get annoyed by me talking a lot my apologies I'm gonna get started with the haircut now just had a lot to talk about all right I hope you guys had a good weekend this haircut like I said it's gonna be a faux-hawk I'm sectioning for me and this haircut is important like always so what I'm gonna do is zoom in on him so you want to find kind of where you want this triangular shape to sit so what I'll do is I'll kind of comb the hair forward and then I'll take a look in the mirror and see exactly where I want that weight to start being removed and where I want it to build up to what this down a little bit what is the difference between a faux-hawk and a mohawk faux-hawk is a fake mohawk right so a mohawk is extreme it's shaved it comes around through here not everybody wants to wear a mohawk which is still I don't understand why because they're awesome but faux-hawk is a more kind of modern take on a mohawk that's a little more user-friendly and to me it comes back some people bring it back to about here so this kind of spikes up in the back and it follows through to the front but the sides are more tapered in a little more traditional kind of feel still has kind of an edgier look to it it's great for kids cuts some men still wear this cut you know it looks good if it's on the right person it fits somebody's style so you just got to look for that but that's the difference all right so now what I'll do is I separate the front and the back so right here down to the ear that's separated and then I'm going to go right here in the front and I'm going to decide where do I want to bring that taper up to we go about right here I'm going to comb this hair over part it and then I'll slide a clip up underneath now I'm going to do the same thing on the side you can see it's kind of on the edge of the eyebrow right there and then we're going to do the same thing on the opposite cross look right about the edge of the eyebrow this hair up way slide that clip up under stay out of your guys's way all right and I'm not worried about the back so much right now so it's going to stop right about that behind the ear kind of that follows a hairline up that's about where I'll stop I'm also going to be fading into that building up that crown area but I'm not really going to hold that part of the haircut in my hand so talk about it all right thank you David I appreciate it see here I'm just going right through here I'm going to block Monica there you go Monica no more all right so here we go now I'm going to blow dry the entire cut so underneath here I'm going to keep this wet on top so I'm going to be cutting that in my hands I'm going to blow dry this just to smooth it out a little bit and also get it dry so I can do my clipper work so I'll use my ergo brush right here diamond head brush it's a smaller brush I'm just going to work this hair down nice and smooth alrighty so now we got it smoothed out so and I saw Lynn was asking she came in a little bit late if I this was cut with clippers yet I haven't cut it yet I haven't cut anything I was talking a little bit at the beginning but this was a previous cut so now I'm going to go in I'm going to cut it shorter so this would be this kind of a typical situation let somebody comes in every four weeks get shorter hair this is grown out just slight bit so I'm going to go in nice and tighter and and cut this cut so I'm going to start off I'm going to actually use a one guard to cut this I'm going to go a little bit tighter than normal and then I want to thank you so much appreciate it Lynn you're welcome how long you've been in this industry I have been cutting hair since 2004 so 17 years now long time not as long as some but longer than a lot alright I'm going to go nice and close here I'm using my and this master clipper this is a cordless clipper love this thing tons of talent here and I'm going to work through now as I go in and clipper I'm just going to pull away right around the ear so I'm not going to take this all the way up I'm not trying to go that tight all the way through this haircut just around these edges I'll comb the hair forward I'm going to start off right here work through and then just flip my wrist out when I get up to that line so in and out here then we'll continue into the back basically what I want to do is I'm holding this weight line here back into the back in that occipital bone area so I'll flip out right when I get to that point sorry just focusing in so I'll flick out right at the occipital bone and this is a one guard all the way open so let's call it maybe a one and a half this would be closed see I'll get shorter open is that way obviously if this is a real person I would move his ear and work my way through that way again up and out when I get to this point so now I'm drawing a curved line around all right now I've got my shortest length cut all right do you prefer clipper over comb to scissor over comb I prefer both so at different situations I'm going to scissor over comb today to kind of work this line in a little bit and take out some of this bolt but a lot of times I like to do both so I really want this haircut to be a lot more scissor detail now there's no reason for me to really go too into the base here with scissors because that would just take forever and you have tools to do it you know you can also your tools to do the top too but for me I can get a little bit more control me personally this is some people have more control clippers I have more control around these edges with either a clipper over comb or scissor over comb work and today I really want to have these like fine-tuned details I don't want to cut a lot of hair at once so that's kind of why I'm choosing to go in this way let me see if I can this will be okay so now the goal here for scissor over comb is to get first off I use a wider tooth comb to do my scissor over comb work so nice firm comb this is a I believe 3 3 6 3 3 7 why is part comb wide teeth nice smooth feel to the comb so it slides through the hair really easy but the teeth aren't too wide to where they kind of grip too much hair together at once either so you get a nice precision feel to it but you can really work that comb up the head shape now as I work up the head I'm gonna start here start removing some of this bulk and then I'll go back through and fine-tune it a little bit more so you just turn so you guys can see I come right here and I'm gonna work through and I'll just see where I'm at with that length so I want more blend than that I'm gonna go up and I'm not trying because it's a faux-hawk I'm not trying to have too much of a wait line at all at this point I actually want to bring this wait line as close to the head as possible so then I can start my triangular feel I don't want to have bulk coming out here it's too bulky then I have to try to make that triangular it's not going to look right so going nice and close to the head again you could clipper all the way up if you wanted to maybe I'll do that on the opposite side show you guys both ways let me know say please do that in the chat say please do that in the chat that'd be great or say scissor over comb all the way whatever you feel like so you can kind of see how that's starting to blend up so same thing here now I turn my comb backwards a little bit and cut up and this length that we're going for here is probably about a three at the top highest point so that's where I'll go clipper wise nice please do that in the chat so specific love it all right so now we scissor over comb through it and that's all good but then when we start to peel back on the head shape getting back around this corner I need to drop so instead of going horizontal like this start to drop more diagonal back and then also I want to keep weight here and I want to build texture in here so I have to make sure that this cut through here just kind of goes straight up and then I can always cut this more into my fingers so try to stay out of that length in that crown area more key thing with scissor over comb is to really just keep the one blade you go here so keep the one blade up against the bone of the comb so just like that and then you close down and you work up the section the hair gets fed into the comb and then you cut down on the hair you don't want to be chomping at it like this because then you'll lose you'll start pushing hair or cutting hair weird this keeps it more mechanical and you just can kind of work through here bone of the comb work through always good to look at somebody straight on in the mirror so you can see the balance of the vertical line as I'm looking here you can kind of see where that little edge is better and then I'm going to go and I'm going to do clipper work over here so best thing to do in my opinion for clipper work I'm going to grab my three guard and I'm going to do it fully open right now actually I'm going to go four guard to get the bulk out and then I'll go three guard probably take it down here so watch watch kind of how the movement works with this clipper guard so as I go up the head so I work up the head like this I follow the head shape and then I continue I don't continue following around I come up and through up and through so the flick of the wrist is also kind of an up and through but at that top point even when I'm here come up I let that hair kind of just fall into the clipper this is how you let the head shape kind of dictate how the way to the haircut flows so that's a four and I really don't mind that length now I'm going to blend it with a three this line here in the midpoint so I go a closed three I'll actually work my way around the head bring up not much to cut here see so we were at about a three guard for this our scissor over comb now for like a lot of people you could just be like all right I'm good with that clipper over comb or that clipper work for me I I'm much more of a scissor kind of guy I use the clipper to do things quickly but I like the control I have with my scissor and it's less bulky for me working around things so I fly through with the clipper but then I'll always go in and do a little extra detail work with scissor over comb so right here I just wanted to shift that line a little bit I go in there and cut I'm gonna let this top out only because not because I'm gonna start cutting it right away but kind of want to see how it's all falling together I kind of like to think about the way that I cut men's hair like hopefully if there's barbers watching I'm not gonna say that I cut with clippers better than most barbers out there but hopefully I can kind of shift and show you guys some shaped things on the top with hairdressers I hope I can show you guys some easier ways to go about clipper work because maybe you guys aren't the best with maneuvering your clippers either so I like to think that that would be the two reasons why each each person would kind of follow what I'm doing here a little scissor over comb around the edges and we got our length in the front we've got texture and length in the back that we haven't cut yet it's subjective agreed this is my clipper side see I brought a little bit extra weight down here I didn't need now I go through scissor over comb bring in a little closer extra weight so now wet down the top and the back we'll start in the back and then we'll work our way towards the front I change up my comb so now I'm gonna go with my 334 comb here and I'll separate front and back and basically what I'm gonna do to cut this faux-hawk is I'm gonna start by creating a guide right here I'm going short to long and I'm gonna start bringing everything over to that point I'm gonna travel a little bit towards the beginning and when I get about midway between the center back and behind the ear I'm gonna stop and I'm gonna start over directing to the center the reason I do that is because I want to start building up weight in the background but I don't want to build up too much weight so that's kind of why I'm gonna make my shift so I go here pivoting sections through the back not gonna create any disconnection so I've got my guideline right there now a key move would be to kind of start point cutting from that short point to the long point cut through now I pivot this new section is gonna go halfway to the previous point cut through I cut that in half now we're halfway there so all these continued new sections till I get to center back we'll go right to that stationary guide last one that middle section okay so now that pushes some of the weight here to the bottom occipital bone area so I'm gonna do the same thing on this side then I'm gonna blend that we'll come over here now I'm gonna stand in front of the client at this point take my section still cutting short to long here longest point will be in that center pivot pull the next section halfway to the previous where at that midpoint pull that one halfway to the previous and then now we're stationary bring it to that stationary guide point cut through center back or just bring it all it's not all gonna reach anyway center back cut through now what have we created we created a slight gradual kind of round line coming back and then it pushes quickly to this very center back so now the very center of this section is the longest point okay so when you look at it it can start to give us this kind of Mohawk feel in the back from a short to long point now we're gonna go into it in a second and blend but that's the goal that we were going for so now I comb this down I can like comb it down I got a nice blend on both sides rounded feel to it but I can just take this little point and cut in just to blend it a little bit more so it's not disconnected it doesn't look like a tail also come over here and you can always cut in and blend just a little bit as well same thing on the side here all right now we're gonna go into the front that's funny so we just ask why do I always say we have no idea not really sure why because it's us and when I teach I figure we're all doing it together it's probably not the case though setting myself up here we are learning together that's right Aryan all right so here we go how do we get this triangular shape on the top I'm gonna take center parting just like this and we're gonna start by cutting the right side our guide is gonna come from this back point that we cut prior so just like this bring it back to that back point I'm gonna cut short to long longest part being in the center now the cool thing about a faux hawk is it doesn't need to be super long right so it's really just about creating that triangular texture now I'm gonna bring this section halfway back to the to the guide I'm gonna continue doing that take a new section bring it halfway back to the guy after I cut this one I will show you guys the front view you guys that are feeling don't know the angle this bring it up halfway back to the previous yes I have a black shirt on you can see that angle so short shorter to longer right there spin him point cutting that would even be better yeah I'm gonna point cut though I just not point cutting right now I'm gonna point cut when I dry it because here's the thing you can always point cut into somebody's hair but you can't put hair back so depending on how thick your client's hair is and what you're actually going for I like to dry it and then put in the the right amount of point cutting as opposed to just point cutting it from the get go wet because wet hair doesn't really tell you exactly what you're you're going for and now all this came back to the previous guys but here's the thing it came back to the previous but once you get to the front of the head the head starts to curve away so the over direction becomes more extreme even though you're not really doing it that's why I don't like to start over directing back too quickly so you can see nice smooth transition through now we're gonna do the same thing on the opposite side standing in front of the client again back to that guide that we cut in the back of the head I'm just gonna cut short to long section halfway back to the guide but so 80-20 barber YouTube on if you knew right away your client had super thick hair obviously I would point cut from the get go so it really just depends on the situation so I totally agree with you in some cases you could definitely just point cut all this is just coming back to what I previously cut last section so now like you would imagine the longest point is in the very front center right there now I'm gonna blow this dry this is long it's longer than I want it to be we've pushed everything into that center so now I want to just make some adjustments I'll blow it dry and then we'll be able to finalize the look so what do you mean by halfway back to the guide cool good question so let me show you so we're working on the top of the head right this is for you guys can see your comments over there too alright you go been on here for a while how's it all right anyways so here you go top of the head right our center parting is right here down and then we took vertical so this let's say with this is where we started this so that becomes section one right then we go here so I'm gonna say here follow through all the way through so what I mean by halfway back right is that if this is one this is one two three four five six seven this is all of our sections what I do is I cut one and that's now my guide right then once you cut one and you grab section two you pull section two back to one and a half what that does is if I pulled section two all the way back to one and cut it now section two is a lot longer than section one now then I pull three back to two and it's even longer than two four back to three it's even longer than three so then all the sudden you basically end up taking these sections through and you end up with a line that quickly goes like this your lengths start shorter and they quickly get long the way that we're trying to do this is because I bring it back you're gonna get more of a line that looks like this across the top still a triangular line still has kind of an upward effect to it but it's not like this which is too much I'm the worst drawer ever which is too much length if you start over directing too much so it's just a way to consistently travel your guide but not over direct it too much through it cool guide to start this haircut should be was this person saying your guide to this haircut should be at the very top of the head from the apex to the bang area how you are going about this cut is ridiculous oh Hera it's fine you don't have to cut it like this and the beauty of the internet is that you don't even have to watch this and the other beauty of this internet is that I don't have to have you watch this so there we go it's the beauty of the world all right um it's okay you're making something so simple and complicated to the extreme I'm not complicating it this is actually the funny thing about this whole thing and I hope that I'm not over complicating it I'm not even trying to overcomplicate I'm trying to oversimplify it so that you guys fully get it so hopefully that's what we're doing the only way I know how to do it and it's fine I'm unknown anonymous I hope that answered your question for sure tell yeah problem solved I like your style thanks yeah literally there's nothing so here's here's the next lesson of the day guys I'm getting older and I don't have time because or nonsense I'm literally just here to teach you guys for free have some fun with you guys enjoy the day there's a lot of negativity in the world and I just don't have time for people that are gonna be negative on the internet and now they're blocked from everything forever so they got to make a new account to come hang with us and honestly I'm not for everybody so and I know that I know that I found one person that I think I'm actually for and she's at my house thankfully all right cool and I don't even like bringing attention to them so I get that too but at the same time it's hard to hard to we can have fun and get rid of it at the same time all right so now I want to go through and I want to cut the top here and I want to take quite a bit of weight or length out of the top because there's no reason for it to be this long so what I'm gonna do is I'm gonna blow it dry real quick get it nice and smoothed out and then that will allow me to really see the overall shape as well Kristen that's fun all right blow dry so this is one of my favorite things is to be able to kind of see the weight within the cut and then make my decisions of how I want to go in and texturize you know like I was talking to a 20 barber on here point cutting is an option to do right away or you could do it a little bit later I'm choosing because I'm gonna point cut through this entire top I also want to show you guys a couple things of the tri razor that can help create some texture as well so the first step is gonna be point cutting second step is gonna be tri razor so we'll go here this and what I'm gonna do is now that I have my overall shape I don't really have to be so perfect in everything that I do I can literally lift this hair up you can see the point actually you can't because I got a black shirt on you can see the point right there I'm gonna turn a little bit so I'm gonna take that hair and in that point I'm gonna point cut into it don't make the point go away that's the whole thing of the haircut that's what makes it kind of mohawk ish so don't make that point go away just point cut into it to soften it you can also remove a little bit of that length if you want I just go in point cut this scissors not loving point cutting today it's got some hair jammed in it also I talked to the virtual cutting club and I was talking about how I use a couple different scissors one for more precision dry cutting work the other one has more of a slide to it so this type of metal it's in my scissor here has more of a glide just feels soft on there when I was just cutting with feels rough because it grips the hair so well which is a good thing but depending on what you're going for right now I wanted to slide so I'm going in point right same thing opposite side just pulling up some of this hair softening that line removing so when I point cut guys I'm really focused mostly on so like I create this pretty blunt line using more precision cutting techniques and all I want to do is just take the edge of that blunt line and soften it if I were to point cut a wet line it would be chunkier right I'm just spit on his head hopefully there's no COVID there um if I were to point cut a wet line it would be a chunkier line it would take out a lot more weight if I just want to soften a line I do it dry because the hair becomes more separated so I can just go in and cut it alright so now what do we do with this front length I pull all this hair up is there a good length for the center of this cut Gary great question I think it just depends on the overall look that your client's going for if or that you're going for but it's too long if you wanted it to kind of stand up and it won't stand up what I like to do is just kind of mess around with the hair move it together in my hands and if it'll actually like stay up with just a little twist of the hair then I know it's at a pretty good length that's if they want to wear it up if they're gonna wear it just kind of messy and all over the place then you know it could be any length just depending but you don't want it to fall flat so I'll hold this hair up I'm gonna go off to one side and I'm actually gonna remove some length from this while shift my scissor over just a little bit like this I'll cut up through do the same thing on the opposite side and then right into the center gonna take just a little bit of this now we're getting there a little extra point cutting through the top go right down the center and just point cutting all right now the name of this mannequin Adele this is Samuel Samuel is his name all right one more thing before the tri-raiser now that we've got everything laying flat in front of the head I'm gonna come in here and I'm just gonna slide and cut is the purpose of the point cutting so Susan purpose of the point cutting is to just soften lines so anytime you go into somebody's hair and you you cut hard precision lines into it a lot of times you're gonna need to go in and just remove some of that weight from the line just to give it a more soft and textured appearance so it's really you know kind of up to you how much point cutting you do or how much point cutting you need to do I am gonna add a little more point cutting to this background area and then the last thing I'm gonna do is you guys know it find my tri-raiser first off a couple of them here so I got tri-raiser right tri-raiser has three different cutting sides this is our patent pending tool that we came out with not too long ago in December came out with it we're shipping it worldwide super fun seeing everybody getting them a couple people said that they got there today somebody in Scotland got it today this razor can create so much texture you got 25% texture side you got a 50% texture you got 100% cutting so you can do precision cuts you do texturizing cuts and then I've got this little velcro clip one of my favorite tools to use on short hair stick it I can stick it to my shirt alright so what I want to do is I want to create a little extra pop of texture in this cut so I like to take diagonal partings stick the velcro clip in the hair like this see how well it holds the hair back and then I can take my texture 25 side of the tri-raiser and hold the hair in my hand this and I'll just take that texture 25 side and work it through either mid shaft or towards the base depending on how thick their hair is you just slide it down and then you remove 25% 25% of the hair and I can do that throughout this cut and so the velcro clips are cool cuz I can just take a bunch of hair clip that in hold it in my hand and then go into it see if I can go the overhead this and I'll do this all over my guys hair take that 25 texture and cut remove bulk take that clip out pop it somewhere else over 25 texture and just remove it now this creates all of that like kind of jagged up and down movement throughout the haircut and I love doing that on this edge of the of a triangular haircut because it just skinnies it up even more and creates again tons of movement in there here 25 texture side 25 texture side right here slide it in even if you only needed some velcro clips these things are awesome because being able to kind of just section hair that quickly in men's cutting like in this lawn just being able to kind of comb a section over stick the clip in and then come through and either scissor over comb or use your texturizing scissor or the tri-raiser just gives you a ton of options last little bit come right here in the front 100% one way and back the other way keeping that longest point in the front 50% especially if you're trying to skinny up a fringe like even if you're using like if this is a female cut or whatever be able to go in and then just kind of grab a section and take 25% and just kind of soften the edges of a fringe just skinnies it up 25 again what kind of technique or cut worse for someone who has a bald spot directly behind your scalp doubles so that feels like a it really in-depth question what I would do is if you could send me pictures of that specific thing I might be able to answer that better I don't know if I fully get it all right so we pretty much got our faux-hawk cut I'm going to hit it with a blow dryer again just to get the loose hairs out and then I'll take a little bit of product and this is something that I'll do in the salon just to just to make sure my client's hair cut is perfect before I rinse them off so a lot of times I'll take like a styling product today I'm gonna use Mitch reformer it's got more of a matte finish there's also Mitch clean cut that one has more of a little bit wetter medium hold finish I like this product actually I want to use this one maybe I'll use this one because I do like the texture in the shine of it I'm gonna use it so here you go fingertip full of the product put it together in my hands and then what I like to do is start with my fingertips and kind of work the product in the hair not and then I'll grab a little bit more from my palms and still kind of work through fingertip wise because if you go right in with your hands all in the hair you're gonna get too much product in one spot so I like to just slowly start working this in start working kind of that mohawk feel to the haircut you guys are really gonna start to see this come to life now then once I get most of that product kind of worked off my hands then I'll start kind of working it through the rest of the cut just to smooth everything down we're gonna brush it out smoothness to it and that would be good there's one so what do you guys think so far why don't you let me know in the chat I raise her just hit a couple points let me zoom in thank you guys alright so just gonna finish up a couple details that is thank you guys appreciate it glad you guys were hanging out let me know if you have questions post them in the comments alright guys thank you very much hope you guys enjoyed the class I will see you guys on the next one will be live tomorrow at 12 30 p.m. Eastern Standard Time we're gonna be doing some women's cutting so I'm excited for that if you guys again have questions post them in the comments we'll definitely get back to you on that and let me know make sure you subscribe I'm trying to read the comments at the same time get an email from me I I'm not sure I don't think I did so try to just send it back resend it and I'll check my email and make sure I get it thank you guys so much make sure that you download the new fsc now app if you haven't done that already it's version 1.6 make sure you're up to date on it get involved in the community go live ask questions you know let's keep building this thing bigger and bigger and again see you tomorrow 12 30 Eastern Standard Time I will try this week with my new tri-raiser awesome that's so cool yeah and if you guys don't have a tri-raiser go pick one up they're super fun to use 4495 on shopfse.com thank you to MinervaBeauty.com for sponsoring the podcast or this pod class or live class whatever you want to say go check out MinervaBeauty.com if you're looking to upgrade your salon furniture they're the best there is with the best prices best shipping all of it so go check it out and that's it thank you guys so much I'll see you tomorrow


We interrupt our regular programming. This is a global emergency Important instructions will follow Oh righty So as everyone in the coaster community just saw Orion's point of view and their grand opening was just released Orion is a new roller coaster that was constructed over at one of Canada's Wonderland's sister parks and also the third Giga to be constructed in the Cedar Fair chain in a recent developments Leviathan at Canada's Wonderland was the original bulgar and Maballard giga coaster to be constructed And is what many people call the test concept for the others to come Fury 325 over at another sister park Carol Wins was developed three years later smashing the records and unveiling an outstanding design fast forward to August 2019 and Enthusiastreams of a giga coaster at Kings Island were finally granted when Cedar Fair announced Orion standing at 287 feet with a drop of 300 feet and speeds of 147 kilometers an hour This brought on many debates of whether it was a giga and some fans being disappointed in the size and length of the coaster Orion cost Cedar Fair roughly 30 million USD and is in large part due to the cost of steel at the time From my personal observations at the time and to date I personally feel like many Enthusiast type themselves up for a much larger project and in doing so Led them to jump to being upset versus analyzing the elements and the rides potential For me, I could instantly tell this was as if Fury 325 and Leviathan were meshed into a new coaster It took what was an amazing on Leviathan and added furies flair and did so in a more compact design to fury The coaster community remained divided on this issue for pretty much the entire offseason and continuing Fast forward to now and Kings Island has released both some absolutely stunning shots of the completed ride Along with an on-ride point of view Also on top of that many people have gotten to visit Kings Island and ride Orion themselves and have provided some Absolutely amazing footage of area 72 and Orion itself I'm going to discuss my observations and opinions of the theming midway and all the aspects over Orion to the best of my ability Thanks to these amazing people. I'm able to show you some absolutely stunning renderings of the overall package and bring it somewhat to life So a huge thank you to Dustin Brennan Brandon and Neek More detailed description will be down below with the names down below as well in the description Let's start with the theming and the midway of Orion at Kings Island As you can see Orion is themed to the park's new area 72 and features the latest prototype vehicle developed by the project X initiative Scientists are in a race against time to develop technology capable of weaving transport vehicles Through the coming meteor storm and traveling to a new planet within the Orion constellation For the program to be successful. It needs volunteers to help with the testing Orion was built next to flight of fear Which is also located in area 72 and received some tender love and care to complement Orion nicely Along with these two roller coasters in area 72 meteor canteen will be located there serving Brout worst with sauerkraut Italian with pepper and onions or hot dog topper off with smoker house chili or cheese sauce or a simple basket of afterburner fries Area 72 is themed to a military base with hangers and a lot of concrete Personally, I love the buildings But so far the little to none greenery is a bit off-putting But once the final project is revealed to the public in a couple days I'll make a final conclusion to the theming. I personally would love to see a lot of rock work a long Orion I think it would complement that space theme and I would like to see a little bit more theming Otherwise with the recent footage that did come out. I'm really impressed with the theming in the queue line for Orion I think they really blew it out of the water Along with analyzing the theming of air sent area 72 and Orion one must look at the lighting package Orion features what looks like a blue LED lighting package up Orion's lift handrail and a changing color Display of floodlights that adds the Orion space theme It is one of the prettiest lift hill displays I've ever seen and I'd say it's the best lighting package on a giga coaster in my opinion to date If you're a photographer, I can only imagine how excited you are to get those specific shots With the station theming and angled upwards toward the lift hill at night time For those that don't know yet Orion will feature both a custom soundtrack by Ima score whom have done soundtracks for Alton Towers and are a fan favorite Personally, this is like the icing on the cake for Orion. You have a beautiful looking coaster What is one of the most brilliant soundtracks and stunning light packages I have ever seen? Just imagine that ambience of waiting in line or in the station at night with a slight breeze and the soundtrack playing as You glance up and see that absolutely gorgeous lighting package and the faint screams of excitement in the distance Let's discuss the trains Another very divided topic in the coaster community. My personal opinion is that they are my least favorite part of Orion. I Would even further state that they are the ugliest train design out of the Cedar Fair giga coasters Looking like a brand deal of toothpaste the Orion trains for me Don't illustrate the theme that the park was after with the latest prototype vehicle It would have been cool to see a more futuristic artistic rendering with more space vehicle type Look on its lead cars for me. If it had that last attention to detail It would be a perfect combo for the best themed giga coaster Curious to hear from you down below in the comment section on your opinions of the theming for Orion This brings us to the coaster itself the main attraction of area 72 Orion as we previously mentioned features a hangar military-styled theme and has somewhat of a pre-show Before you climb up the stairs to the loading platform It was wildly rumored that Orion would feature bins moving above the station's loading area to hold guest belongings But it appears they've opted out and have gone with lockers instead Orion features a lift hill with an amazing lighting package that complements your chain lift climb to 287 feet tall Orion was built in a valley with varying terrain This is what creates that 300 foot drop with a top speed of 91 miles per hour and further complements the various elements to come Orion's second element standing at 174 feet tall is a wave turn styled element that actually appears to pack a much bigger punch Than even I was expecting This leads to a reverse treble clef element standing at 202 feet tall and yet again the pacing in the footage out So far remains extremely well paced Standing at 56 feet tall the speed hill appears to pack the biggest punch on the ride as the Upstop wheels really do their job and hold the train in place as it soars through this close to the ground airtime hill Giving the greatest amount of airtime on the ride Orion then brings you into a well paced massive airtime hill standing at 147 feet tall Again the terrain that Orion utilizes really seems to complement this coaster really well as the pacing seems to remain unaffected during the ride cycle Then comes the ampersand which some at Kings Island have called one of the best or underrated elements with the speeds In which you enter this element The ampersand stands at 125 feet tall and leads into the two remaining airtime moments standing at 90 feet tall Followed by 83 feet tall and from what I can tell from the footage and the reviews coming out that last airtime hill Also packs and a massive amount of airtime. We're even hearing ejector being used Like its sister coasters Orion features a very long brake run which helps it run three trains without a mid-course brake run and allows the train to gradually come to a stop Orion really is amazing element after amazing element taking what Leviathan and fury did amazing and Turned it into Orion the pacing on Orion is absolutely amazing so far from what we can see Based off of the on-ride point of views and the off-ride footage that has come out by Kings Island and other various youtubers It looks like it's an absolutely stunning and amazing coaster based off of the footage What is your favorite element on Orion? With all this said and done the history of Orion and Kings Island is quite an interesting one from rumors surrounding a giga coaster for many years Giga drawn into the snow Driving enthusiasts absolutely crazy and the beast reborn Conspiracy theories King's Island has been quite the rumor mill for quite some time Early blueprints for Orion leaked and there was quite the debate in the coaster community on whether the blueprints were legitimate Slowly everyone ended up figuring out they were and both excitement and anger came out of the shadows Some like myself were really excited about the seventh giga coaster and some felt gypped and confused by the short layout With the cost of steel and a history of roller coasters not boosting attendance too much at Kings Island Many argued this was a very amazing addition for them It was unfortunate timing as Kings Island announced the closure of vortex their beloved arrow coaster at the park Just after seeing firehawk removed for Orion With the removal of vortex some are already looking to what's next What do you honestly think could be next for Kings Island? Thank you for taking time out of your day to watch our video on Orion at Kings Island Hopefully you're able to get out there safely sometime soon and experience it and review it for yourself Hopefully you enjoyed today's video leave a comment down below and don't forget to drop a like If you have any roller coaster or theme park that you would like us to review or go in-depth about their future editions Past editions biggest mistakes or anything leave a comment down below and we'll be sure to check it out Thank you so much for watching and hopefully you have an amazing weekend. Thanks again. Bye


Hi everyone, welcome back to my channel. I hope you're good today! We're going to talk about all of my summer book recommendations. So these are the books that I think are without a doubt perfect for summer. Perfect for summer. Like the books I would recommend. You read the summer, get them on your TBRs. It's a pretty self-explanatory video. We don't need to discuss it anymore. Should we speed it up a little bit? I woke up this morning and like the sun was shining for once. The sun was shining, blue skies, and then I sit down to film and there's a massive gray card in front of me. It is miffing me off somewhat. I really thought I was about to be like sunbathing, like looking so summery. No, look at it.  This is actually not funny. Look at that! Excuse me, why are you so rude? Anyway, but before we get any further in today's video, I want to thank the sponsor for today's video, which is Skillshare. So I'm your Skillshare for years and years. I've loved it for years and years. Way before I had my channel, I think it's such a great place to develop creative skills, whether it's something you like are already kind of good at and want to develop further, or whether it's like a skill you've literally never touched, but you're like, I'm going to give her a go. I'm going to give her a go. Basically, it's this online learning community with classes for every, every, every, every skill or hobby you can imagine. Like literally everything.  Like literally test it, search for a skill that you think is not going to be on there. There'll be a class for it. There'll be a class for it. I kid you not. You can learn languages, photography, illustration, cake decorating. I mean, look at this. They have a cookie decorating class for beginners. Excuse me? What? I love it so much. I'm going to do that class when I go back home. So if like me, you want to use this summer to develop new skills and hobbies like cake decorating, I'd really recommend you go and check it out via the link below. And the first 1000 of you to use the link will have a free premium membership to Skillshare. Honestly, you have nothing to lose.  Why not? It's free. And just give it a go. Have a little peruse, have a little searchy, searchy and see if there's anything that tickles your fancy. There's no ads. They're always launching new classes. And once the membership ends, it's actually very affordable under $10 for a month. So give it a go. I've always loved Skillshare for years and years. I think it's such a great place to learn new things. So I'd really recommend it. Okay, books. Let's talk about the books. Now this was very, very hard to not make these all contemporaries. Summer is contemporary season, like without a doubt. But I was looking at all the books I've read. Why are literally all Miss Susan Thrillers set in the winter? They love November. November is thriller season. Summer, you're only getting contemporaries. Like that's it. No, it's true. It's true. Okay, first things first, I'm not going to speak about it for long. Don't worry, we'll get past this one quick. But you need to read Heartstopper this season. You need to read the graphic novel series Heartstopper. I know this cover is wintery. This one kind of is set in the winter. But volume three, the one before this is set in the summer. And on the whole, it's a summery read. This is a graphic novel series with Nick and Charlie, who are two boys that form in love and love each other. And I'll put the other covers here, particularly volume three, because that is the one that's like super summery.  I just posted a reading vlog for this one, volume four, which I'll link if you want to see it. But it's just so soft, so hot. He fills my heart with warmth. Like genuinely, the best summer read, you could just literally go sit in your garden with the stack of all four and just read them and just have the best time. Like genuinely, I wish probably wishes I'd never read them to this summer. I could read them again. I'm probably going to reread them at some point because I love them so much. And they just bring me so much joy and they're just so easy to read. And I just love them. But genuinely, if you want a joyful, happy, story full of love, it's a graphic novel, won't take you long to read. It's just pictures. Read it. Next, I'm going to recommend this isn't like content. Well, it's kind of, it's like fabulism, magical realism kind of thing. I'm going to recommend You Must Not Miss by Katrina Leno. Now this was an absolute surprise book. I was not expecting to love this as much as I did. Basically, it's about a girl, I think her name's Magpie. Am I right? Yeah, I think her name's Magpie. She has been through a lot of trauma. She's been through a lot of really difficult stuff lately. And this is struggling. And she kind of makes up this magical world. Is it called near? I don't have it with me, so I can't check the details. But she makes up this magical world in her head in this notebook. And then she finds out that she can actually enter this world through her garage, not a garage, like shed door. Like her shed opens up into this world. It's very strange. It's very strange.  It's like the perfect amount of weird. It's such a fast-paced moving book. There are trigger warnings for like sexual assault in this. It is a heavy hitting book, but it's like, it's not afraid to get angry. I really admire how it's not afraid to get angry and really show that anger like unapologetically. I think so often girls in fiction who have gone through trauma are expected to be sad when that's not the only valid response to just going through something difficult and anger is equally valid. And I just love how this book wasn't afraid to go there. I loved how weird and wacky it was. And I'm pretty sure it's set like in the summer. Like I remember her and her friend like going to their swimming pool in the back garden a lot. So it definitely has that summer vibes. I feel like it's hot with anger and with heat and everything. And I loved this. This was such a surprise. Next let's talk about a middle grade. And that is me, my dad and the end of the rainbow by Benjamin Dean. Oh my god, this is so cute. This is so cute. This is so cute. Okay. So this is about a boy named Archie and his parents have just split up. They've been arguing a lot and he doesn't really understand why. And then one day he sees a pride leaflet fall out of his dad's pocket and he decides that he's going to go to this thing called pride in London. He hopes that that's going to fix him and his dad's, not fix him and his dad's relationship, but he just feels like it's not quite right because there's been change. So he just hopes that this will kind of put everything right in his eyes between him and his dad. And so it's the story of him learning about sexuality in the LGBT community. It's beautiful. I think this is such an important middle grade for kids to have out there. But I think it's also such an important book for everyone of every age to read. It's just beautiful. Like it's just a heartwarming story. The album's amazing song to song. I can't stress it enough. Going to Pride nearer the end of the book is such a fun experience. We have drag queens, we have parades. You know when you read a middle grade and it makes you feel like a kid again, I think that's something this book does so well. So I'd really recommend it set in summer. Just a joy filled book. So another book I read recently and think would be perfect for summer. I don't know if this actually occurs in summer. I don't know. But I think it's a really great summer read is The Traveling Cat Chronicles by Hero Arakawa. I, oh lord. I don't want to cry over this book. I don't want to cry over this book. I cried a lot at this. I cried a lot. Now people don't recommend usually like heart breaking books for summer. But I think this is the perfect book to like read in a day in the garden.  Little cry. I don't think you could not cry on reading this. But it's like short and such a quick easy read that I think is perfect for summer. So basically we're following a cat and him and his owner traveling around Japan. This is translated from Japanese because his owner needs to give him away and we don't really know why. And so the owner is going around to some of his friends and we're basically hearing about his owner's backstory. But then the cat, then we'll switch to the cat's perspective and the cat will be like just pissed off about something. The way this perfectly captured a cat's like pissed off perspective was everything. If you have cats, if you love cats, you have to read this. Listen to what I have to say because I'm right. Like I never knew how much I wanted to read from a cat's perspective before until now. Until now. It was so good. I just every, I said in that video, I'll link the reading vlog where I cried and went into detail about this. I said in that video how badly I want every book to be written from a cat's perspective. Like every book, I need like a companion novel from a cat like watching this and being like Too much drama for me. Too much drama for me. So listen, you may not want to cry in the summer. I think every season is crying season if you want it to be. And it is heartwarming at the same time as being heartbreaking, but I can just imagine sitting in the garden, the wind, the sun on me and just like just give me a little read. So yeah, definitely pick this up if you love cats. Next one may, okay, it may take some people off guard, but Catherine House by Elizabeth Thomas. I haven't spoken about this book for a while. I loved it. Now before we talk about this, no, this is like one of the most almighty books ever. You either love it or you hate it.  Like it's really unhinged. It's very strange, but I loved it. Our main character gets to attend the school called Catherine House, which is really prestigious, but you have to go there for like three or four years and you're not allowed any contact with the outside world during that time.  There's there's no way to explain this book.  It is sporadic. It's confused as a book. And it's such a weird writing style. But I think if you want a bit of like a challenge this summer, read Catherine House because this does obviously encapsulate many years. So it goes through the seasons, but I have a distinct memory of the role that like heat played in the summer sectioned in this book and how claustrophobic this book feels reminds me of that. The book feels very hot and claustrophobic. So listen, you may not want that as a summer vibe, but like it can't all be contemporary to you guys. It can't all be contemporaries. Sometimes we have to switch it up a little, a little bit of something for the summer. What did she say? Something fun for the summer? Something fun, something for the summer time, something for the girls, so you know, get ready and party. One of the strange books I've ever read, I do want to reread it. It just did something. It just went there. It really went there. It really tried its best. I love Catherine House. If you're looking for a weird book, give it a go. Don't be afraid. Like you may hate it or you may absolutely be obsessed with it. And that's just the risk you've got to take. And then the last book I would recommend for the summer is with the fire on high by Lisbeth Attavedo. This was, I think, the only contemporary in my favourite books of last year.  And it's about her figuring out her responsibilities to that was also trying to like live the life that she wants to live as a teenager in high school. She loves to cook and there's this cooking class that she wants to take but it involves this trip away. And so it's just about that and how that conflicts with the way that her life has had to become. Food plays such a big role in this book. Like if you like food, this book is gonna make you hungry. I loved her love of cooking and how that was explored. It, Lisbeth Attavedo, her other two books are like poetry format. Is it verse? Ren in verse? I'm pretty sure. I always get them mixed up and people always make fun of me. Listen. It's almost hurtful to me to watch her be so dumb. But this one is like told more as a traditional book and I just felt like you've got so much time to spend with the characters and learn about them and really become attached to them. Lisbeth Attavedo's writing is beautiful. It has this lyricalness to it and I loved it. So maybe I feel like this is the least popular of Lisbeth Attavedo's books. The Poet X, I would say is the most popular and I feel like people don't read this one enough. So it's perfect for summer. I think I read it like around the time of last summer and it just has this lightness and this fun to it whilst also discussing difficult topics. So there we have it. That is the books I'd recommend you read this summer. Let me know what is on your summer TBR, what you're planning to get to this summer and also if you have any recommendations for books that you think are perfect to read in the summer because I always want the recommendations. We know this. If you've gotten to the end, comment a sunshine emoji and I will see you very soon in another video. Bye!


So, welcome back. My pleasure to introduce Supratik. Supratik is a professor here at IIT Bombay, so he is technically one of your hosts. And Supratik is going to talk about knowledge compilation for Boolean functional synthesis. But Supratik is a person I think if those of you who are looking to do a PhD in the area, I think he should be one of your prime candidates to go and try to do a PhD with him, right? So, Pratik I have given you an open inventory, sort of open endorsement. Of course, if you want to do a, if you don't want to do it with Supratik, please come and do it with me. Yeah, thanks Sanjeeva for the introduction. So, I am going to talk about some recent work that we have been doing on Boolean functional synthesis that is also a poster on this outside. So, let me try to quickly sort of describe the problem and some of the results that we have. This is part of ongoing work and this is work with Akshay and Sheetal are certainly here. I don't know if Krishna is here and some of our students Jatin and Divya who have since graduated. So, what is Boolean functional synthesis? So, Boolean functions are of course very important if you all know that. Now, sometimes it is difficult to specify the behavior of a system as a function and sometimes it is easier to specify it relationally. So, here is a sort of simple example that everybody can relate to that suppose I want to describe an arbiter which has two inputs, request inputs and two grant outputs and I want to specify how the grant output should be, what is the behavior of the grant outputs in terms of the request inputs and it might be actually easier to specify it in this manner saying that as long as there is one, as long as there is at least one request at least one grant should be high. Both the grant should not be simultaneously high, this is trying to arbitrate between two requests to a specific resource let us say. And if grant 1 is high then request 1 should have been high and if grant 2 is high then request 2 should have been high. And so, if you look at the way I have described the behavior of the system over here, I am basically saying that I do not know what G1 is as a function of R1 and R2, I do not know what G2 as a function of R1 and R2, but I would like the system to behave in this way. So, that this is the relation between the inputs and outputs and so, this kind of specification is also called relational specification and this is convenient to specify, but once I give you the specification you still have to synthesize that arbiter. So, you have to get G1 and G2 in terms of R1 and R2 and that is the problem that we want to address. So, we want to synthesize Boolean functions from a relational specification, everything is Boolean here there is no temporal aspect and this problem we will call the Boolean functional synthesis problem. So, the formal definition is so, we are given some blue inputs and some red outputs and we are given a relation between the blue inputs and the red outputs and we want to synthesize some functions 1 fj for each output yj such that if you read this thing it is saying for every value of the inputs if there exists a way of assigning values to the outputs such that the specification can be met then these functions substituted for these outputs will also satisfy the specification. So, it would you know one would normally think that this implication should be in one direction because if there is an output then I want the functions, but the implication in the other direction comes for free. I mean if you already have f1 to fm which satisfies this then of course, there exists y1 to ym. So, it is an equivalence and these fj's are also called Scholem functions in the literature and this is when when an important point to note that it is possible that for some values of x1 to xn there may not be any values for y1 to ym such that phi can be satisfied. But even in that case even in you know such problem instances this makes sense because this is saying that for all those other values for which there exists y1 to ym f1 to fm should be such that it satisfies the specification for those x1 to xn for which there does not exist any y1 to ym there is nothing that can be done. So, even if for some x1 to xn there is not anything such that which satisfies this problem still makes sense as long as there are some x1 to xn for which it makes sense to talk about some outputs. So, I want to make this distinction clear because this does make a difference in some of the techniques and the technique that we are going to talk about actually works even in such cases. So, there are several applications of Boolean functional synthesis I will not go through all of them I have just you know for the sake of time I have just you know put up a long list and this is certainly not a comprehensive list there are several other things and there are kind of important applications like quantifier elimination certifying solvers basically if you give a quantified Boolean formula and if you want to know whether it is satisfiable or not then you also need a certificate to show you know I mean this morning we heard a lot about proofs. So, these certificates form part of the proof for QBF it is used for program synthesis repair of circuits programs tons of things and we are certainly not the only ones to work on this problem. In fact, it looks like Boole worked on it George Boole as early as 1847 and Lowenham you know several of you might have studied about Lowenham's Column theorem. So, you know so this has been basically looked at by stalwarts since long there are I mean of course, and they did come up with solutions which are very theoretical which if you try to implement them they do not scale in practice. There are people who have tried to say that ok let us look at this formula for all x x is y y x y and if this formula turns out to be valid which means that for every x there is indeed a y which is not always the case as I just mentioned. But if this formula turns out to be valid we can then look at the proof of validity of that formula and from there we can extract Scholem functions. So, people have worked on that templates we have heard about templates a lot yesterday that has also been used to generate Scholem functions. There are some function composition based approaches which Watt tried you know towards the beginning of the current resurgence and interest in this area. It turns out that this method is you know nice to learn nice to study but if you have large number of outputs to synthesize this tends to blow up. Using binary decision diagrams this has been tried and Rohr is here he is he has also worked in this and this scales for a class of benchmarks as long as we have good variable orders for BDDs that is always the problem if you do not have good variable orders then this performance degradation. Recently there has been work on incremental determinization Sanjit has worked on it and this also works well for a large class of inputs and in fact this restriction was there earlier but now it has been removed. So, it now works even if for some x is there are no y's and then there are quantifier instantiation techniques there is recently some work that we did along with Rohr and Moshe Varthy and Luca Tabahara on input output separation and some earlier work that we have done where we try to come up with a informed estimate of what the Scholem function should look like and then we try to fix them iteratively. So, the talk I am going to talk about today is none of these it is about a completely different approach and before we get into that let us try to understand what led us to you know even trying to get into this business of knowledge compilation. So, last year in some work that Akshay Shetil and I and a few students did we try to ask the question that how hard or easy is this problem and some results are you know fairly easy to see that if I give you a pi to p problem then if I could synthesize Scholem functions for these I could just substitute them back into the formula and then invoke a co-np oracle and I would be able to solve this. So, a co-np to the np problem or a pi to p problem can be solved if I had a solution if I had something which could solve the Boolean function synthesis problem. So, this is not really an oracle, but if it could give me the solution to this I could use that to solve this problem. So, at least we know that it is at least np hard cannot be simpler than that, but then we also ask that well this np hardness is really talking about the time how much time can it take, but suppose I gave you all the time that you needed how small can you get these Scholem functions, what is a lower bound on how small can these functions be. So, in particular we are asking does there exist compact Scholem functions although synthesizing may take any amount of time exponential or even beyond of course an exponential time we can synthesize. So, of course when we are talking about this the first thing that comes to mind is that aren't there already lower bound results on circuit sizes. So, it turns out that yes of course it is very seminal work on lower bound results on circuit sizes, but they refer to monotone circuits and we are not putting the restriction that the Scholem functions that we synthesize have to be monotone and therefore these arguments do not really carry over here. So, we have to use some other arguments to show to find lower bounds for the lower bounds of the Scholem functions you know as much time as you can take, but how small can we get these functions. So, this led us last year to sort of arrive at these results we were able to show that unless the polynomial hierarchy in complexity theory unless it collapses to the second level there will exist relational specifications for which one cannot get Scholem functions which are polynomial size they have to be super polynomial. Now, does the polynomial hierarchy collapse to the second level I certainly don't know that nobody knows that as of today it is unlikely it is one of the long standing open questions, but if we say that that is unlikely then it this is also unlikely that we will get polynomial size Scholem functions always. Then we were also able to show that this is another hypothesis in complexity theory the non-uniform exponential time hypothesis I will not go into the details of the hypothesis, but unless this long standing hypothesis fails there exist specifications for which Scholem functions must necessarily be exponential sized ok. So, that is the bad news which basically means that efficient algorithms that always give us the answer in polynomial size are unlikely, but then the good news that we also saw in that we were able to show in the same paper is that if the specification is given in some kind of normal forms and we identified this one form in that paper called weak decomposible negation normal form then it is indeed solvable in polynomial time and space. So, what is this weak decomposible negation normal form you know very at a very high level it means that if I can express the specification as a circuit such that if I take any literal and the negation of the literal and there are two paths meeting up at an AND gate then that is called weak decomposible negation normal form. It turns out that every Boolean function can always be expressed in this form in weak decomposible negation normal form, but there might be an exponential blow up in the size ok. So, this is what we had last year and this basically and you know we did a lot of experiments which showed that interestingly that efficient synthesis was possible not only when the specification was in this form, but even when the specification was not in this form and that led us to ask that something more interesting is going on I mean this is certainly not a strong characterization of when we can do efficient synthesis. So, that led us to ask this questions that is there a weaker representation form that guarantees poly time synthesis and we came up with a positive answer to that that yes there is something weaker which is which we call the synthesis negation normal form that guarantees poly time synthesis and not only that it actually subsumes and is exponentially more succinct than several other representation forms that are there in the literature. Then the next question we asked is that given a specification f is it possible to simplify that specification and still solve the original problem and this also we were able to answer affirmatively and using a notion of refinement that I will explain in the subsequent slides and finally, can be algorithmically compiled f compile f to a refined synonym f spec f prime synonym f would guarantee polynomial synthesis and refinement would ensure that whatever we are doing would still solve the original problem even though the problem I might be solving is for a new problem for a refinement of the and this also we were able to show affirmatively. But of course, given the lower bounds we know that there is no escaping this I mean this somewhere we have to there are no free lunches somewhere we have to be. Okay. So, this led us to ask that basically can we do this compilation given a specification f can we compile it to a specific form which has some properties because after that then we can do everything efficiently. So, in the literature this field of study is also called knowledge compilation and in particular this is Wikipedia's definition which says that it is a family of techniques for addressing the interactability of a number of artificial intelligence problems. This is the specific reference to artificial intelligence and a propositional model is compiled in an offline phase to support some difficult queries in poly time once it is compiled. And so, the only change that we do. So, essentially the picture is this that you take a propositional formula in whatever form you compile it to a specific form for these artificial intelligence problems and after that in poly time you can answer some difficult questions like how many solutions are there to the original formula was the original formula satisfiable, what are all the models of the original formula and so on. So, this part is guaranteed poly time this is the compiler and in the AI context a lot of work has happened to convert you know formulas for example, in CNF to formulas in DNNF, BTDs whatever there is a whole bunch of other things. So, in our context we just change the definition to say that well we are not talking about a specific artificial intelligence problem although it can be applied to some AI problems but we are talking about a synthesis problem. So, the picture looks something like this that you have given a specification in one of these forms and you are also told what are the inputs and outputs because that does matter just the Boolean formula is not sufficient I need to know I should synthesize what in terms of what and then can I compile it down to a normal form. So, this is our synthesis normal form so is that after that in poly time we can actually get the Scholem functions. So, the focus of the stock is really on this because after that everything is easy. So, here is a quick introduction and I will certainly not be able to do justice to all that went into proving the results but I hope to be able to at least convey the idea of what is going on. So, suppose I am given a specification phi on the inputs x and outputs y and suppose I represent it as a negation normal form circuit directed acyclic graph. So, what is negation normal form it is a circuit which has only AND and OR gates all the NOT gates are at the leaves. So, for example, if here if this is Boolean function then this is the negation normal form of this is already written negation normal form. So, that all the negations that appear are at the leaves beyond that there are only AND and OR gates. So, what we do is we say ok you give me a specification and I look at it in its negation normal form circuit or DAG and this is actually an easy translation. For example, if you give me any Boolean circuit I can use de Morgan's law to push the negations down and this can be done in poly time this is usually no problem. What we do next is we say that ok once I have this I am going to transform this a little bit and to get what we call a positive form of the specification. So, in this positive form of the specification I will have the inputs I will have the outputs and I will have some additional stuff over here which and as many of those as there are outputs and these additional stuff are basically obtained by replacing every negation y i leaf by a fresh variable y i bar. So, for example, this was the formula we had earlier. So, for every place where I have negation of an output I am going to introduce a y i bar negation of an output y i bar. So, in terms of the circuit it just means that at these two places I had some negation y 2 and negation y 1. So, I am going to put y 2 bar and y 1 bar ok. So, because the NNF circuit could be obtained easily this can also be obtained easily and this is called positive form of the formula and actually this is also not new this has been studied in the literature we found out later although we sort of reinvented the field here. Now, it turns out that this positive form has some nice properties and I think it is best represented through this picture. So, if I take the formula phi and if I look at its positive form and let us say I want to existentially quantify out one of the output variables y 1 ok. So, it turns out that if I take the positive form and set both y 1 and y 1 bar remember the negation y 1s have been replaced by fresh variables. So, now I can assign them values independently. So, if I replace both of them by 0 I always get an under approximation of this and if I replace both of them by 1 I always get an over approximation of this and this is not very deep I mean if you just look at how you know for this basically I have you know both are 0 then you know I am sort of saying that I might be even cases where it might become true because this was set to 1 I am going to disallow those and here because both are 1 even cases where this might become 0 because one of them has to be 0 I am sort of allowing those. So, this is not very hard to see that I can actually obtain over and under approximations of existentially quantifying out one of the output variables by just setting constants to chosen leaves of this positive form. Now, it turns out that we can do something more and in fact, for example, if I want to quantify out both the outputs I just set all of them to 0 and set all of them to 1 and I get upper and over approximations under and over approximations. Now, it turns out that if I start off with this positive form of the specification I can actually try to sort of see whether this is going to be good for synthesis purposes and towards that end what we will do is we will start off with the positive form of the specification and we will start off with a linear ordering of the outputs. How we get this linear ordering is you will get a flavor of it in you know the next slide itself, but let us not get into that you know that problem the optimal ordering finding the optimal ordering is indeed hard. So, what I am going to do is I am going to say let me take this positive form and let me fix y 1 till y i minus 1 and y 1 bar till y i minus 1 bar all to 1s. This is kind of the same trick that I showed in the earlier slide where I want to set a variable and its negation now renamed to the same value and these other things y i plus 1 to y m and y y i negation y i plus 1 to negation y m. So, these over line these bar variables I am just setting to the negation of this. So, if I take this positive form and if I do this transformation I will get a formula in terms of the x's in terms of y i y i bar and in terms of y i plus 1 to y m. So, now we ask that does there exist any value of x 1 to x n and y i plus 1 to y m which makes this positive form semantically equivalent to y i and y i bar. So, the reason why we are asking this question are all technical details in the paper, but as you can see this is just a query to a SAT solver nothing more than that. I am asking does there exist any assignment of these values which will make this positive form equivalent to y i and y i bar. Remember y i bar is not the same as negation y i it is a renamed variable whereas all the other things here I have kept the negation of these and these things here have assigned the same value to this. So, essentially we are asking can you know can this formula be made to behave like y i and y i bar and if the answer is no if we cannot make it behave like y i and y i bar for all i in 1 to n then we say that this formula is in syn-NNF. In fact, this phi hat then is good enough for poly-time synthesis and I will just show you how that happens. So, here is a simple example to sort of illustrate that complicated definition. So, here is a formula on some inputs and outputs here it is actually CNF formula here is the circuit representation and note that this is you know for those who are aware of what DNNF is this is not in DNNF because you have an AND gate and you have things like y 2 and negation y 2 going and meeting up there. It is not in weak DNNF also for the same reason y 2 and negation y 2 can go and meet up there. So, this is not one of the forms that you know we had studied earlier, but now let us say I fixed this output ordering. So, let us say you know this is a linear ordering I fixed this linear ordering and then I want to ask that well can I make this behave like y 1 and y 1 bar is there a way that I can assign values to the other things is that I can make it behave like y 1 and y 1 bar clearly no because there is no y 1 bar here at all right. So, the answer is I cannot make it behave like y 1 and y 1 bar. So, that is good news. So, then I ask that can I make it behave like y 2 and y 2 bar after changing this to y 2 bar, but before asking the question I am allowed to set y 1 and y 1 bar to 1s that is what we had said here I am allowed to set these two 1s. So, it is not the same as just asking can I make this behave like y 2 and y 2 bar I am asking that after I have set y 1 and there is no y 1 bar here after I have set it to 1 can I now make it behave like y 2 and y 2 bar and it turns out that I cannot because that 1 here blocks off this y 2 it does not let that y 2 reach that AND gate. So, therefore, this is in synNNF with respect to this ordering if I flip the ordering is it still in synNNF. So, here I am asking can I make it behave like y 2 and y 2 bar first and sure I can. So, it is not in synNNF with respect to this ordering. So, it is a fairly delicate notion the same structure for a certain ordering can be in synNNF may not be in synNNF and remember the result that I said earlier once we know it is in synNNF we have poly time synthesis. So, this ordering does matter when we are doing the synthesis. So, here are some relations to other data structures other representations we know for example, if this is a binary decision diagram then actually it can be converted in linear time to something which is synNNF basically every node in the BDD needs to be replaced by the structure and here you see y 1 bar do not ever go and meet a better AND gate they always go and meet a better OR gate. So, every BDD can be converted in linear time to a synNNF which means that if you can just construct a BDD for your specification that is it you are done you have poly time synthesis. It does not depend on the order of variables in the BDD for example, it could be a BDD with any arbitrary order, but once you have. So, you know for a BDD for every possible ordering of the variables it is in synNNF for every possible ordering of the variables in the synNNF definition, but of course when you are constructing the BDD you have to come up with some order. So, here you come up with any order does not have to be input first input last whatever any order which works I can immediately convert it to this and here you can see that no variable and its negation will ever go and meet up at an AND gate. So, it does not matter what order you chose for the synNNF definition they will for every possible order. So, if you start from a BDD and construct this circuit in linear time for every possible output ordering it is in synNNF. So, this relaxes the freedom of what ordering I can use to construct this BDD it does not have to be input first right. So, DNNF is of course you know it is very widely studied in the AI literature decomposable negation normal form. So, it says that for every AND gate that you have in the circuit representation the leaves here and the leaves on the the leaves at the bottom of the two sub trees rooted at the two children of that AND gate they must be completely disjoint right. So, if z appears here where z is either an input or output or whatever that neither z nor negation z can appear here. So, this is DNNF. So, of course, if it is in DNNF it is certainly in synNNF weak DNNF said that well ok if y appears here then y bar should not appear here. So, of course, if it is in weak DNNF then certainly in synNNF, but synNNF is even if y and y bar have you know I mean for example, if x and negation x have a path to something it does not matter I mean I showed that example where y2 and y2 bar actually go and meet up an AND gate, but still it is in synNNF because you are allowed to fix the values of some of the other variables earlier alright. So, DNNF, WDNNF are already in synNNF. So, so it looked like synNNF has kind of generalized a few of the earlier things and then we asked this question that did it really generalized or are these only a few cases could it be the case that in some case synNNF becomes larger than these other representations and then we had these results which basically said that there exist polynomial size synNNF specifications that can be expressed using BDDs only in exponential size using DDNNF only in exponential size super polynomial size unless once again some complexity theory conjecture gets falsified and so on, but it is also true that there are representations for which you can get NNF representations just plain vanilla NNF which are polynomial size, but the synNNF representation can be super polynomial and once again this is coming out from the lower bound that we have I mean we cannot escape this ok. So, this is kind of the ordering that we have NNFs are the most compact that we know then we have synNNF which are strictly more succinct than WDNNF which is strictly more succinct than DNNF this is deterministic decomposable negation normal form and then BDDs. So, BDDs are really at the far extreme end whereas, these are you know almost at the other end ok. So, how does synNNF helps column function synthesis? So, here is a template for once you have this thing in synNNF remember you will have some I think the colors got interchanged the output should be red and the input should have been blue, but once you have the specification in synNNF all you do is you know the first thing you do is you set all of them except the last one to ones. So, here in this case there are two outputs I will set y1 and y1 bar to 1 and y2 and y2 bar the last output to 1 0 and this guarantees that I will get a column function for y1 for y2 and once I have the column function for y2 I can then take another copy of this and now at y2 I can feed this already. So, this dotted line means feeding y2 this dotted line means feeding negation of y2 y2 and negation of y2 and then I do the same thing. So, for all output variables except the last one I am going to set the output and its bar both to 1 and the last output I will set it to 1 and 0 and then I get this column function for the next variable and I can just keep continuing doing this. So, it is not hard to see that if you do this you can basically now get all the column functions that you wanted in how much size as many outputs in the worst case you will have to replicate it that many times. So, m times the size of the specification and how many additional wires do you need. So, here you know this guy needs to go not only to the next one, but to the one after that to the one after that. So, it is like you know the output from this needs to go to m minus 1 the output from this needs to go to m and so on. So, there are order m squared additional wires. So, everything is poly time, poly time and poly space because that was the main question we were trying to ask that can we make it polynomial sized ok. Now, so that is good. So, that I think is the you know gist of what Sinin and F is and then there is this other question that we wanted to ask is that is it possible to simplify the specification and still get an answer to the original question. And so, here I have pictorially represented in this form. So, suppose I am given the specification phi of x y and let us say this blue region represents all those values of x for which actually there exists a y. So, that phi of x y is true. And let us say this represents the space of all scolium functions that I could have substituted. So, once again this x should have been blue the space of all scolium functions for y. So, every point within this space is a scolium function for y that I could use and every point within this space is a valuation of x for which there exists a y. So, if I am given a spec and if this is the view with respect to the valuations of x and the possible scolium functions we are saying that well can I get another spec phi tilde which may expand this it is not required to be the same as this, but can only shrink this. So, what is this saying? It is saying that every scolium function for phi tilde is also going to be a scolium function for phi. And the scolium function for phi tilde may actually this specification may be satisfiable in a larger range for a larger subset of inputs than the original specification. So, if I can find a phi tilde which does this you know expanding possibly expanding this and possibly shrinking this then I will call that a refinement with respect to synthesis of phi. And in this case we can just solve the problem for phi tilde and that will be a solution of the original problem. It turns out that if I do not allow this to expand beyond the set of x's and I say that well phi tilde must also evaluate to the values of x for which phi tilde xy can be made true is the same as the values of x for which phi could be made true, but this has possibly shrunk. So, that is called a stronger refinement and it turns out that these notions are very useful and in particular we have this lemma which says that if I have a specification which refines another specification then every scolium function that I synthesize for this specification is also a scolium function for the other specification and the same is true even for strong refinement. So, here is a simple example this might be by original specification looks quite big. This specification can be shown to satisfy the properties I just showed relative to this and so this is a refinement with respect to synthesis of this and so it is perfectly fine to synthesize the scolium functions from here and if you look at it you can just set y1 to 1 and y2 to 1 and you are done. So, setting y1 to 1 and y2 to 1 also implements this specification you can see that each clause turns out to be true. So, we put it all together in a tool which takes in a specification in CNF or an inverter graphs and it outputs a refined phi tilde which is already in CNNF. It uses some kind of branching I think Mate told a lot today about how branching is done you know similar techniques are used heuristics are used it aggressively tries to refine wherever possible because refinement can only simplify things for us and the details are in the paper and I will just maybe go to this last slide saying that you know we need not look at that. So, if you just look at these plots we tried to compare the time taken by C2SIN which is the tool that we have with a BDD compiler which takes a specification compile sit down to a BDD because once it is a BDD we know it is simple after that but C2SIN is not necessarily BDD. We tried to compare it with KDIT which is the incremental determination based tool which is I think the best tool that we have today and some earlier work that we did BFSS I know Kuldeep has recently come up with another work we did not have it when we did this comparison. So, but he has a comparison of that in the poster and so the picture here is and these are different kinds of benchmarks from the QBF eval suit and also from some factorization benchmarks. So, I think the story here is that I think no one method is better than the other methods and which is what is to be expected for hard problems, but you know there are clearly methods where there are clearly problem instances where the other methods seem to fail I mean they are timing out here whereas this going through the CINNNF compilation step works whereas going through the CINNNF compilation step also fails in some cases where the other things work. So, I think this is just to be thought of as another technique in the portfolio of techniques of Boolean functional synthesis the nice part about it is that we can now give some formal guarantees that it is polynomial time and size in terms of the CINNNF representation and anything that we can do to improve the compilation to CINNNF can only help in this process being fully cognizant of the fact that there are super polynomial lower bounds lurking in there. So, we will not be able to go polynomial unless some complexity conjectures has falsified I will stop there and take any questions. How do you order your why and what happens if you order it does not lead to anything? Do you backtrack try another one or? Do we backtrack and find another order? Yes. No, actually finding the best order is something that we have not solved so far but what we do is the following. So, the algorithm what it does is it takes a CINNF formula and then it says that these are the output variables which I have to eventually ensure that this property holds and then it asks which is the output variable that you would have split on if you are trying to solve let us say satisfiability question. So, we look at the VCID score for example for the output variables and then we say okay let us branch on this output variable because the moment we branch we basically have an if then else kind of structure and then we know that that variable is taken care of and the residues are themselves simplified and then we go ahead and ask can we so the first thing we do is we ask can we refine this to sort of simplify it further. Yeah, because you show an example depending of the order you find something or not. This one, this one. So, it happens that in your case you may use the wrong order and you will not succeed, right? No, no, no if I use the wrong order I will just become a bigger CINNNF. I will always succeed it is like I am branching, right? Okay. So, every time I choose a variable and branch on it I am basically creating an if then else structure and the moment you create an if then else structure it is yeah. So, it is basically this. So, this always satisfies CINNNF. The question is did I branch on the right variable first?  Yeah, this specific structure is not in CINNNF with respect to this order. Yes. But now if I want to convert it to CINNNF with respect to this order I will just split on y2 first. So, I will get a different structure that structure will be bigger than the structure and then that will be in CINNNF, right? And for example, if I split with respect to y2 I will get y2 and whatever something or negation y2 and something. So, that structure which is not the same as this, this does not have the form of y2 and something or negation y2 and something. That structure is already in CINNNF because of this that you know y and negation y can never go and meet up. So, any order will always give you a CINNNF. Is it giving you something which is small? So, this is the usual question how do you use a variable order. Okay. Thanks, Suprati. Okay.