Cycle Height of Finite Automata

  • Chris KeelerEmail author
  • Kai Salomaa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10952)


A nondeterministic finite automaton (NFA) A has cycle height \(\mathcal {K}\) if any computation of A can visit at most \(\mathcal {K}\) cycles, and A has finite cycle height if it has cycle height \(\mathcal {K}\) for some \(\mathcal {K}\). We give a polynomial time algorithm to decide whether an NFA has finite cycle height and, in the positive case, to compute its optimal cycle height. Nondeterministic finite automata of finite cycle height recognize the polynomial density regular languages.



Research supported by NSERC grant OGP0147224.


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© IFIP International Federation for Information Processing 2018

Authors and Affiliations

  1. 1.School of ComputingQueen’s UniversityKingstonCanada

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