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 σ 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 non-deterministic time is in subexponential deterministic time and also separates N L from P . Furthermore, under a (more general) non-uniform variant

more »

... f the assumption mentioned above we can prove that N L = N P .