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Lower Bounds for the Transition Complexity of NFAs

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Mathematical Foundations of Computer Science 2006 (MFCS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4162))

Abstract

We construct regular languages L n , n ≥1, such that any NFA recognizing L n needs \(\Omega( {\rm nsc}(L_n) \cdot \sqrt{{\rm nsc}(L_n)})\) transitions where nsc(L n ) is the nondeterministic state complexity of L n . Also, we study trade-offs between the number of states and the number of transitions of an NFA. We show that adding one additional state can result in significant reductions in the number of transitions and that there exist regular languages L n , n ≥2, where the transition minimal NFA for L n has more than c nsc(L n ) states, for some constant c > 1.

Research supported, in part, by the Natural Sciences and Engineering Research Council of Canada.

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Author information

Authors and Affiliations

  1. Jodrey School of Computer Science, Acadia University, Wolfville, Nova Scotia, B4P 2R6, Canada

    Michael Domaratzki

  2. School of Computing, Queen’s University, Kingston, Ontario, K7L 3N6, Canada

    Kai Salomaa

Authors
  1. Michael Domaratzki
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  2. Kai Salomaa
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Comenius University, Mlynská dolina, 84248, Bratislava, Slovakia

    Rastislav Královič

  2. Institute of Informatics, University of Warsaw, Poland

    Paweł Urzyczyn

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Domaratzki, M., Salomaa, K. (2006). Lower Bounds for the Transition Complexity of NFAs. In: Královič, R., Urzyczyn, P. (eds) Mathematical Foundations of Computer Science 2006. MFCS 2006. Lecture Notes in Computer Science, vol 4162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11821069_28

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  • DOI: https://doi.org/10.1007/11821069_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37791-7

  • Online ISBN: 978-3-540-37793-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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