Um, a fixed set of inputs cannot be of arbitrary length, since you by definition know the size of the longest possible input string. The point is that a functi

Um, a fixed set of inputs cannot be of arbitrary length, since you by definition know the size of the longest possible input string. The point is that a function cannot bijectively compress arbitrary input into fixed output. Of course if you make the function itself depend on the input itself, then you can pull all sorts of tricks, but normally we do not call a simple lookup table a 'hash function', because they are very different things.