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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 To build an automaton, simply call translate() with a formula, and a list of options to characterize the automaton you want (those options have the same name as the long options name of the ltl2tgba tool, and they can be abbreviated).
Step1:  The call the spot.setup() in the first cells has installed a default style for the graphviz output.  If you want to change this style temporarily, you can call the show(style) method explicitely.  For instance here is a vertical layout with the default font of GraphViz.
Step2:  If you want to add some style options to the existing one, pass a dot to the show() function in addition to your own style options
Step3:  The translate() function can also be called with a formula object.  Either as a function, or as a method.
Step4:  When used as a method, all the arguments are translation options.  Here is a monitor
Step5:  The following three cells show a formulas for which it makes a difference to select 'small' or 'deterministic'.
Step6:  Here is how to build an unambiguous automaton
Step7:  Compare with the standard translation
Step8:  And here is the automaton above with state-based acceptance
Step9:  Some example of running the self-loopization algorithm on an automaton
Step10:  Reading from file (see automaton-io.ipynb for more examples).
Step11:  Explicit determinization after translation
Step12:  Determinization by translate().  The generic option allows any acceptance condition to be used instead of the default generalized Büchi.
Step13:  Adding an automatic proposition to all edges
Step14:  Adding an atomic proposition to the edge between 0 and 1
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Python Code:
a = spot.translate('(a U b) & GFc & GFd', 'BA', 'complete'); a
Explanation: To build an automaton, simply call translate() with a formula, and a list of options to characterize the automaton you want (those options have the same name as the long options name of the ltl2tgba tool, and they can be abbreviated).
End of explanation
a.show("v")
Explanation: The call the spot.setup() in the first cells has installed a default style for the graphviz output.  If you want to change this style temporarily, you can call the show(style) method explicitely.  For instance here is a vertical layout with the default font of GraphViz.
End of explanation
a.show(".ast")
Explanation: If you want to add some style options to the existing one, pass a dot to the show() function in addition to your own style options:
End of explanation
f = spot.formula('a U b'); f
spot.translate(f)
f.translate()
Explanation: The translate() function can also be called with a formula object.  Either as a function, or as a method.
End of explanation
f.translate('mon')
Explanation: When used as a method, all the arguments are translation options.  Here is a monitor:
End of explanation
f = spot.formula('Ga | Gb | Gc'); f
f.translate('ba', 'small').show('.v')
f.translate('ba', 'det').show('v.')
Explanation: The following three cells show a formulas for which it makes a difference to select 'small' or 'deterministic'.
End of explanation
spot.translate('GFa -> GFb', 'unambig')
Explanation: Here is how to build an unambiguous automaton:
End of explanation
spot.translate('GFa -> GFb')
Explanation: Compare with the standard translation:
End of explanation
spot.translate('GFa -> GFb', 'sbacc')
Explanation: And here is the automaton above with state-based acceptance:
End of explanation
a = spot.translate('F(a & X(!a &Xb))', "any"); a
spot.sl(a)
a.is_empty()
Explanation: Some example of running the self-loopization algorithm on an automaton:
End of explanation
%%file example1.aut
HOA: v1
States: 3
Start: 0
AP: 2 "a" "b"
acc-name: Buchi
Acceptance: 4 Inf(0)&Fin(1)&Fin(3) | Inf(2)&Inf(3) | Inf(1)
--BODY--
State: 0 {3}
[t] 0
[0] 1 {1}
[!0] 2 {0}
State: 1 {3}
[1] 0
[0&1] 1 {0}
[!0&1] 2 {2}
State: 2
[!1] 0
[0&!1] 1 {0}
[!0&!1] 2 {0}
--END--
a = spot.automaton('example1.aut')
display(a.show('.a'))
display(spot.remove_fin(a).show('.a'))
display(a.postprocess('TGBA', 'complete').show('.a'))
display(a.postprocess('BA'))
!rm example1.aut
spot.complete(a)
spot.complete(spot.translate('Ga'))
# Using +1 in the display options is a convient way to shift the 
# set numbers in the output, as an aid in reading the product.
a1 = spot.translate('a W c'); display(a1.show('.bat'))
a2 = spot.translate('a U b'); display(a2.show('.bat+1'))
# the product should display pairs of states, unless asked not to (using 1).
p = spot.product(a1, a2); display(p.show('.bat')); display(p.show('.bat1'))
Explanation: Reading from file (see automaton-io.ipynb for more examples).
End of explanation
a = spot.translate('FGa')
display(a)
display(a.is_deterministic())
spot.tgba_determinize(a).show('.ba')
Explanation: Explicit determinization after translation:
End of explanation
aut = spot.translate('FGa', 'generic', 'deterministic'); aut
Explanation: Determinization by translate().  The generic option allows any acceptance condition to be used instead of the default generalized Büchi.
End of explanation
import buddy
b = buddy.bdd_ithvar(aut.register_ap('b'))
for e in aut.edges():
    e.cond &= b
aut
Explanation: Adding an automatic proposition to all edges
End of explanation
c = buddy.bdd_ithvar(aut.register_ap('c'))
for e in aut.out(0):
    if e.dst == 1:
        e.cond &= c
aut
Explanation: Adding an atomic proposition to the edge between 0 and 1:
End of explanation
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