Regular expression not containing 101
<p>I <a href="http://www.public.asu.edu/~ccolbou/src/355hw2s12sol.pdf">came across</a> the regular expression not containing 101 as follows:</p>

<blockquote>
  <p>0<sup>∗</sup>1<sup>∗</sup>0<sup>∗</sup>+(1+00+000)<sup>∗</sup>+(0<sup>+</sup>1<sup>+</sup>0<sup>+</sup>)<sup>∗</sup></p>
</blockquote>

<p>I was unable to understand how the author come up with this regex. So I just thought of string which did not contain 101: </p>

<blockquote>
  <p>01000100</p>
</blockquote>

<p>I seems that above string will not be matched by above regex. But I was unsure. So tried translating to equivalent pcre regex <a href="https://www.regex101.com/r/fA2oY1/1">on regex101.com</a>, but failed there too (as it can be seen my regex does not even matches string containing single 1. </p>

<p>Whats wrong with my translation? Is above regex indeed correct? If not what will be the correct regex?</p>