Re: A Regexp Assembler/Compiler

Given a set of regexps and given a wanted logical concatenation (lets start with AND,OR) of these regexps, is there any mechanism to create a smaller, more eficient set of regexps that will have the same effect?

Very unlikely given the power of Perl regular expressions. One of the questions that you would need to answer is whether two grammars (I use grammar here instead of regular expression to avoid confusion later on) are equivalent; that is, whether the will match the same language (where a language is the set of all strings matched by a grammar). For regular expressions (not Perl regular expressions, but for traditional ones) this question is decidable. But for more powerful grammars on the Chomsky hierarchy, this question is undecidable.

However, Perl regular expressions are hard to place on the Chomsky hierarchy. Without (?{ }) or (??{ }), Perl regular expressions cannot be used to create all context free grammars (take the language of strings with balanced parenthesis for instance). On the other hand, it can be used to create grammars that are context sensitive on the Chomsky hierarchy. (With (?{ }) it could very well be that Perl regular expressions are at least as powerful as context free grammars, but I don't see an obvious proof.)

My guts say that such a mechanism does not exist, that the problem is unsolvable. If the problem is solvable, it's going to be incredibly hard.

Abigail

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Re(2): A Regexp Assembler/Compiler by gumby (Scribe) on Jun 19, 2002 at 15:29 UTC
I don't think that there is anything wrong in posing this question in the language of boolean logic and set theory. Any solution set of the above subroutine will be the union of the complement of the solution set of the first regexp and the solution sets of the other regexps. Although finding a regexp whose solution set this is would be non-trivial, as Abigail-II points out.	[reply]
Re(3): A Regexp Assembler/Compiler by gumby (Scribe) on Jun 19, 2002 at 15:56 UTC
On further reflection, it's actually quite likely that algorithms have been developed for similar problems (ie. Boolean algebra's, elimination theory etc.).	[reply]
Re: Re: A Regexp Assembler/Compiler by PetaMem (Priest) on Jun 19, 2002 at 20:53 UTC
My guts say that such a mechanism does not exist, that the problem is unsolvable. If the problem is solvable, it's going to be incredibly hard. I agree with Abigails intuition here, but only for the language space perl regexps span in general. Considering the examples I've given above, one sees, that there are regexps (hard ones) and regexps (next to trivial). So my guts tell me, that for a certain subset of regexps this problem must have a more or less achievable solution, the more expression you'd like to handle the more "incredibly hard" it will get. But hey - then again it'll be just incredibly possible if you allow me the `s///ing` of a well known citation. :-) Bye PetaMem	[reply] [d/l]