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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 variantdoi:10.1109/ccc.2000.856753 dblp:conf/coco/KarakostasLV00 fatcat:n7usfnux35fbni4grr4ejeqqzy