On the complexity of intersecting finite state automata and [formula omitted] versus [formula omitted

Abstract

We consider uniform and non-uniform assumptions for the hardness of an explicit problem from finite state automata theory. First we show that a small improvement in the known straightforward algorithm for this problem can be used to design faster algorithms for subset sum and factoring, and improved deterministic simulations for non-deterministic time. On the other hand, we can use the same improved algorithm for our FSA problem to prove complexity class separation results ( NL is not equal to P , or NP for the non-uniform case). This result can be viewed either as a hardness result for the FSA intersection problem, or as a method for separating NL from P or NP . It is interesting to note that this approach is based on a more general method for separating two complexity classes, using algorithms rather than lower bounds.