The Complexity of Intersecting Finite Automata Having Few Final States
The problem of determining whether several finite automata accept a common word is closely related to the well-studied membership problem in transformation monoids. We review the complexity of the intersection problem and raise the issue of limiting the number of final states in the automata involved. In particular, we consider commutative automata with at most two final states and we partially elucidate the complexity of their intersection nonemptiness and related problems.
KeywordsAbelian Group Permutation Group Membership Problem Commutative Monoids Unary Language
Unable to display preview. Download preview PDF.
- [Bea88b]Beaudry, M.: Membership testing in transformation monoids. PhD thesis, McGill University (1988)Google Scholar
- [BLS87]Babai, L., Luks, E.M., Seress, A.: Permutation groups in NC. In: Proc. 19th Annual ACM Symposium on Theory of Computing, pp. 409–420 (1987)Google Scholar
- [FHL80]Furst, M.L., Hopcroft, J.E., Luks, E.M.: Polynomial-time algorithms for permutation groups. In: FOCS, pp. 36–41 (1980)Google Scholar
- [GJ79]Garey, M.R., Johnson, D.S.: Computers and intractability: a guide to the theory of NP-completeness. W. H. Freeman and Company (1979)Google Scholar
- [Knu81]Knuth, D.E.: The art of computer programming: seminumerical algorithms, 2nd edn., vol. 2. Addison-Wesley (1981)Google Scholar
- [Koz77]Kozen, D.: Lower bounds for natural proof systems. In: Proc. 18th Annual Symposium on Foundations of Computer Science, pp. 254–266 (1977)Google Scholar
- [Luk86]Luks, E.M.: Parallel algorithms for permutation groups and graph isomorphism. In: FOCS, pp. 292–302. IEEE Computer Society (1986)Google Scholar
- [Luk90]Luks, E.M.: Lectures on polynomial-time computation in groups. Technical report. College of Computer Science, Northeastern University (1990)Google Scholar
- [Rei05]Reingold, O.: Undirected st-connectivity in log-space. In: Proc. 37th Annual ACM Symposium on Theory of Computing, pp. 376–385 (2005)Google Scholar