A Multivariate Analysis of Some DFA Problems

  • Henning Fernau
  • Pinar Heggernes
  • Yngve Villanger
Conference paper

DOI: 10.1007/978-3-642-37064-9_25

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7810)
Cite this paper as:
Fernau H., Heggernes P., Villanger Y. (2013) A Multivariate Analysis of Some DFA Problems. In: Dediu AH., Martín-Vide C., Truthe B. (eds) Language and Automata Theory and Applications. LATA 2013. Lecture Notes in Computer Science, vol 7810. Springer, Berlin, Heidelberg

Abstract

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.

Keywords

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Henning Fernau
    • 1
  • Pinar Heggernes
    • 2
  • Yngve Villanger
    • 2
  1. 1.Department of InformaticsUniversity of TrierGermany
  2. 2.Department of InformaticsUniversity of BergenNorway

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