Language and Automata Theory and Applications

Volume 7810 of the series Lecture Notes in Computer Science pp 275-286

A Multivariate Analysis of Some DFA Problems

  • Henning FernauAffiliated withDepartment of Informatics, University of Trier
  • , Pinar HeggernesAffiliated withDepartment of Informatics, University of Bergen
  • , Yngve VillangerAffiliated withDepartment of Informatics, University of Bergen

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We initiate a multivariate analysis of two well-known NPhard decision problems on DFAs: the problem of finding a short synchronizing word and that of finding a DFA on few states consistent with a given sample of the intended language and its complement. For both problems, we study natural parameterizations and classify them with the tools provided by Parameterized Complexity. Somewhat surprisingly, in both cases, rather simple FPT algorithms can be shown to be optimal, mostly assuming the (Strong) Exponential Time Hypothesis.


Deterministic finite automata NP-hard decision problems synchronizing word consistency problem