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Measures of Nondeterminism in Finite Automata

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Automata, Languages and Programming (ICALP 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1853))

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Abstract

While deterministic finite automata seem to be well understood, surprisingly many important problems concerning nondeterministic finite automata (nfa’s) remain open. One such problem area is the study of different measures of nondeterminism in finite automata. Our results are:

  1. 1.

    There is an exponential gap in the number of states between unambiguous nfa’s and general nfa’s. Moreover, deterministic communication complexity provides lower bounds on the size of unambiguous nfa’s.

  2. 2.

    For an nfa A we consider the complexity measures advice a(n) as the number of advice bits, ambig A(n) as the number of accepting computations, and leaf A(n) as the number of computations for worst case inputs of size n. These measures are correlated as follows (assuming that the nfa A has at most one “terminally rejecting” state): advice A(n),ambig A(n) ≤ leaf A(n) ≤ O(advice A(n) ⋅ ambig A(n)).

  3. 3.

    leafA(n) is always either a constant, between linear and polynomial in n, or exponential in n.

  4. 4.

    There is a language for which there is an exponential size gap between nfa’s with exponential leaf number/ambiguity and nfa’s with polynomial leaf number/ambiguity. There also is a family of languages KON m 2 such that there is an exponential size gap between nfa’s with polynomial leaf number/ambiguity and nfa’s with ambiguity m.

Supported by DFG grant Hr-1413-2 and Finland-Germany Project “Descriptional Complexity and Efficient Transformations of Formal Languages over Words, Trees, and Graphs”.

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Author information

Authors and Affiliations

  1. Lehrstuhl für Informatik I, RWTH Aachen, Ahornstraße 55, 52074, Aachen, Germany

    Juraj Hromkovič & Sebastian Seibert

  2. Department of Mathematics, University of Turku, Finland

    Juhani Karhumäki

  3. FB Informatik, Johann-Wolfgang-Goethe-Universität, 60054, Frankfurt am Main, Germany

    Hartmut Klauck & Georg Schnitger

Authors
  1. Juraj Hromkovič
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  2. Juhani Karhumäki
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  3. Hartmut Klauck
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  4. Georg Schnitger
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  5. Sebastian Seibert
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Editor information

Editors and Affiliations

  1. Department of Computer Sciences, University of Pisa, Corso Italia, 40, 56125, Pisa, Italy

    Ugo Montanari

  2. Center for Computer Sciences, University of Geneva, 24, Rue Général Dufour, 1211, Geneva 4, Switzerland

    José D. P. Rolim

  3. Department of Computer Sciences, ETH Zurich, 8092, Zurich, Switzerland

    Emo Welzl

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© 2000 Springer-Verlag Berlin Heidelberg

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Hromkovič, J., Karhumäki, J., Klauck, H., Schnitger, G., Seibert, S. (2000). Measures of Nondeterminism in Finite Automata. In: Montanari, U., Rolim, J.D.P., Welzl, E. (eds) Automata, Languages and Programming. ICALP 2000. Lecture Notes in Computer Science, vol 1853. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45022-X_17

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  • DOI: https://doi.org/10.1007/3-540-45022-X_17

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  • Print ISBN: 978-3-540-67715-4

  • Online ISBN: 978-3-540-45022-1

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