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 k where 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 NL from P. Furthermore, under a (more general) non-uniform variant of the assumption mentioned above we can prove that NL = NP.

• Type: Conference
• Year: 2000
• Where: COCO
• Authors: George Karakostas, Richard J. Lipton, Anastasios Viglas
• Keywords: Algorithms, COCO 2000, Intersection Emptiness Problem, Straightforward Algorithm, Subexponential Deterministic Time