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.