The crossword solution for the term 'PROBLEM FOR SYLVESTER THE CAT' is 'LISP', which stands for 'LISt Processing'. It is a computer programming language that was developed in 1958 by John McCarthy and is used for artificial intelligence applications. It is a high-level language, meaning it is designed to be easier for humans to read and write than other programming languages. Sylvester the Cat is a Looney Tunes character who is often seen trying to catch Tweety Bird, so it is likely that the problem he is facing is related to this pursuit.