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On the Emptiness Problem for Two-Way NFA with One Reversal-Bounded Counter

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Algorithms and Computation (ISAAC 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2518))

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Abstract

We show that the emptiness problem for two-way nondeterministic finite automata augmented with one reversal-bounded counter (i.e., the counter alternates between nondecreasing and nonincreasing modes a fixed number of times) operating on bounded languages (i.e., subsets of w 1 * ...w k * for some nonnull words w1,..., w k) is decidable, settling an open problem in [11,12]. The proof is a rather involved reduction to the solution of a special class of Diophantine systems of degree 2 via a class of programs called two-phase programs. The result has applications to verification of infinite state systems.

The work by Oscar H. Ibarra has been supported in part by NSF Grant IIS-0101134.

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Author information

Authors and Affiliations

  1. School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA, 99164, USA

    Zhe Dang

  2. Department of Computer Science, University of California, Santa Barbara, CA, 93106, USA

    Oscar H. Ibarra

  3. Department of Mathematics, Nanjing University, Nanjing, 210093, China

    Zhi-Wei Sun

Authors
  1. Zhe Dang
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  2. Oscar H. Ibarra
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  3. Zhi-Wei Sun
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Editor information

Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada, K1S 5B6

    Prosenjit Bose  & Pat Morin  & 

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Dang, Z., Ibarra, O.H., Sun, ZW. (2002). On the Emptiness Problem for Two-Way NFA with One Reversal-Bounded Counter. In: Bose, P., Morin, P. (eds) Algorithms and Computation. ISAAC 2002. Lecture Notes in Computer Science, vol 2518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36136-7_10

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  • DOI: https://doi.org/10.1007/3-540-36136-7_10

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