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On the Complexity and Decidability of Some Problems Involving Shuffle

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Descriptional Complexity of Formal Systems (DCFS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9118))

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Abstract

The complexity and decidability of various decision problems involving the shuffle operation (denoted by ) are studied. The following three problems are all shown to be \(\mathsf{NP}\)-complete: given a nondeterministic finite automaton (\(\mathsf{NFA}\)) \(M\), and two words \(u\) and \(v\), is , is , and is ? It is also shown that there is a polynomial-time algorithm to determine, for \(\mathsf{NFA}\)s \(M_1, M_2\) and a deterministic pushdown automaton \(M_3\), whether . The same is true when \(M_1, M_2,M_3\) are one-way nondeterministic \(l\)-reversal-bounded \(k\)-counter machines, with \(M_3\) being deterministic. Other decidability and complexity results are presented for testing whether given languages \(L_1, L_2\) and \(L\) from various languages families satisfy .

The research of O. H. Ibarra was supported, in part, by NSF Grant CCF-1117708.

The research of I. McQuillan was supported, in part, by the Natural Sciences and Engineering Research Council of Canada.

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Author information

Authors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508 TB, Utrecht, The Netherlands

    Joey Eremondi

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

    Oscar H. Ibarra

  3. Department of Computer Science, University of Saskatchewan, Saskatoon, SK, S7N 5A9, Canada

    Ian McQuillan

Authors
  1. Joey Eremondi
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  2. Oscar H. Ibarra
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  3. Ian McQuillan
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Corresponding author

Correspondence to Ian McQuillan .

Editor information

Editors and Affiliations

  1. School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada

    Jeffrey Shallit

  2. Department of Mathematics, University of Turku, Turku, Finland

    Alexander Okhotin

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Eremondi, J., Ibarra, O.H., McQuillan, I. (2015). On the Complexity and Decidability of Some Problems Involving Shuffle. In: Shallit, J., Okhotin, A. (eds) Descriptional Complexity of Formal Systems. DCFS 2015. Lecture Notes in Computer Science(), vol 9118. Springer, Cham. https://doi.org/10.1007/978-3-319-19225-3_9

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  • DOI: https://doi.org/10.1007/978-3-319-19225-3_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19224-6

  • Online ISBN: 978-3-319-19225-3

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