Says fundflow:
if memory serves, regexp equivalence is not an easy question
You are absolutely right. Very little is known about regexes. What little is known indicates that the problems are all very hard.

(is it in NP? someone can surely fill up on that)
It is probably not in NP, but nobody knows for sure. Regex inequivalence ("Given two regexes, do they represent different languages?") is known to be PSPACE-complete. PSPACE-complete problems are at least has hard as NP-complete problems, but probably harder. If the regexes contain only the concatenation and | operators (no *'s), the problem is "only" NP-complete.

See (of course) Garey & Johnson Computers and Intractibility, p. 267.

In reply to Re: Regexp Speed Concerns by Dominus
in thread Regexp Speed Concerns by tadman

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.