The Complexity of Finding Reset Words in Finite Automata

  • Jörg Olschewski
  • Michael Ummels
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6281)


We study several problems related to finding reset words in deterministic finite automata. In particular, we establish that the problem of deciding whether a shortest reset word has length k is complete for the complexity class DP. This result answers a question posed by Volkov. For the search problems of finding a shortest reset word and the length of a shortest reset word, we establish membership in the complexity classes FPNP and FPNP[log], respectively. Moreover, we show that both these problems are hard for FPNP[log]. Finally, we observe that computing a reset word of a given length is FNP-complete.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jörg Olschewski
    • 1
    • 2
  • Michael Ummels
    • 2
    • 3
  1. 1.Lehrstuhl Informatik 7RWTH Aachen UniversityGermany
  2. 2.LSV, CNRS & ENS CachanFrance
  3. 3.Mathematische Grundlagen der InformatikRWTH Aachen UniversityGermany

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