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Safety Verification for Two-Way Finite Automata with Monotonic Counters

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Developments in Language Theory (DLT 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2450))

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Abstract

We look at a model of a two-way nondeterministic finite automaton augmented with monotonic counters operating on inputs of the form \( a_1^{i_1 } ...a_n^{i_n } \) for some fixed n and distinct symbols a 1,…, a n, where i 1,…, i n are nonnegative integers. Our results concern the following Presburger safety verification problem: Given a machine M, a state q, and a Presburger relation E over counter values, is there (i 1,…, i n ) such that M, when started in its initial state on the left end of the input \( a_1^{i_1 } ...a_n^{i_n } \) with all counters initially zero, reaches some configuration where the state is q and the counter values satisfy E? We give positive and negative results for different variations and generalizations of the model (e.g., augmenting the model with reversal-bounded counters, discrete clocks, etc.). In particular, we settle an open problem in [10]

The work by Oscar H. Ibarra has been supported in part by NSF Grants IIS-0101134 and CCR02-08595.

Corresponding author (ibarra@cs.ucsb.edu).

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Author information

Authors and Affiliations

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

    Oscar H. Ibarra

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

    Zhe Dang

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

    Zhi-Wei Sun

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

Editors and Affiliations

  1. Faculty of Science and Faculty of Engineering, Kyoto Sangyo University, 603-8555, Kyoto, Japan

    Masami Ito  & Masafumi Toyama  & 

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Ibarra, O.H., Dang, Z., Sun, ZW. (2003). Safety Verification for Two-Way Finite Automata with Monotonic Counters. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2002. Lecture Notes in Computer Science, vol 2450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45005-X_29

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  • DOI: https://doi.org/10.1007/3-540-45005-X_29

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  • Print ISBN: 978-3-540-40431-6

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