/aa([^a]|a[^a])*aa/
In general it's a pain to write a regular expression not containing a particular string. We had to do this for models of computation - you take an NFA, which is easy enough to define, and then reduce it to a regular expression. The expression for things not containing "cat" was about 80 characters long.
Edit: I just finished and yes, it's:
aa([^a] | a[^a])aa
Here is a very brief tutorial. I found some great ones before, but I can't see them anymore.
All you need is a reluctant quantifier:
regex: /aa.*?aa/
aabbabcaabda => aabbabcaa
aaaaaabda => aaaa
aabbabcaabda => aabbabcaa
aababaaaabdaa => aababaa, aabdaa
You could use negative lookahead, too, but in this case it's just a more verbose way accomplish the same thing. Also, it's a little trickier than gpojd made it out to be. The lookahead has to be applied at each position before the dot is allowed to consume the next character.
/aa(?:(?!aa).)*aa/
As for the approach suggested by Claudiu and finnw, it'll work okay when the sentinel string is only two characters long, but (as Claudiu acknowledged) it's too unwieldy for longer strings.
By the power of Google :-p I found a blogpost from 2007 which gives the following regex that matches string which don't contain a certain substring:
^((?!my string).)*$
It works as follows: it looks for zero or more (*) characters (.) which are not preceeded (?! - negative lookbehind) by your string and it stipulates that the entire string must be made up of such characters (by using the ^ and $ anchors). Or to put it an other way:
The entire string must be made up of characters which are not preceded by a given string, which means that the string doesn't contain the given substring.