I do not know, but I did some internet research and found the following:

*PostgreSQL*: supports POSIX style regexps, described to great detail in: 
http://www.postgresql.org/docs/9.0/static/functions-matching.html
*MySQL*: supports a style "which is aimed at conformance with POSIX 
1003.2", described here: http://dev.mysql.com/doc/refman/5.1/en/regexp.html
*Oracle*: supports "IEEE Portable Operating System Interface (POSIX) 
standard draft 1003.2/D11.2", described: 
http://docs.oracle.com/cd/B19306_01/appdev.102/b14251/adfns_regexp.htm
*MSSQL*: not sure, I think you probably need to define a function on your 
own using CLR language (?).
*FireBird*: Support RegExp, but didn't specify according to which syntax 
exactly. Details: 
http://www.firebirdsql.org/rlsnotesh/rlsnotes25.html#rnfb25-dml-regex
*DB2*: Need to implement a function that does it, details: 
http://www.ibm.com/developerworks/data/library/techarticle/0301stolze/0301stolze.html
*Informix, Ingres*: Not sure, wasn't able to find something definitive, but 
probably need to extend the language to support regexps.

In addition I found the following article of someone who explored the 
regexp support of popular SQL databases: 
http://trentrichardson.com/2008/10/23/exploring-various-sql-regex-syntax/

All in all, seems that most systems support some version of POSIX standard, 
except when you need to extend the SQL with a user defined function, then I 
guess you can chose the implementation you want.

Hope this help,
Omri

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