On the complexity of intersecting finite state automata

We consider the problem of testing whether the intersection of a collection of k automata is empty. The straightforward algorithm for solving this problem runs in time σ^k where a is the size of the automata. In this work we prove that the assumption that there exists a better algorithm solving the FSA intersection emptiness problem implies that nondeterministic time is in subexponential deterministic time and also separates NL from P. Furthermore, under a (more general) non-uniform variant of the assumption mentioned above we can prove that NL≠NP