**From:** Hans Aberg (*haberg@math.su.se*)

**Date:** Sat Oct 13 2007 - 16:11:03 CDT

**Previous message:**Andreas Stötzner: "Re: Emoticons (was: Root and fraction (2 new symbols))"**In reply to:**Philippe Verdy: "RE: FYI: Regex paper for UTC"**Next in thread:**Philippe Verdy: "RE: FYI: Regex paper for UTC"**Reply:**Philippe Verdy: "RE: FYI: Regex paper for UTC"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

On 13 Oct 2007, at 21:36, Philippe Verdy wrote:

*> ...such operation is typically used in association with [an] operator
*

*> that restricts the set of matchable strings.
*

You might merely add operations that correspond to the set operations

of the languages, and let the user figure out their usability. L(x|y)

is already the union of L(x) and L(y). And if, for a natural number

k, L(x^k) = L(x)^k, then one can extract all strings of length k to

complement against (see below).

So let L(x&y) be the intersection of L(x) and L(y), L(~x) the set

complement of L(x), L(x \ y) = L(x) \ L(y) (set difference).

Then, if "." matches all characters, all strings of length 2 that do

not match "ab" can be gotten from .^2 \ "ab" (or .^2 & ~"ab"). If U

is the set of legal Unicode strings, and U_k the subset of strings of

Unicode length 2 (which might be different from the string length),

then all Unicode strings of Unicode length 2 that do not match "ab"

can be gotten from U_2 \ "ab".

Mostly, one would use the set difference \ operator, rather than the

complement ~.

Hans Ĺberg

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