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Quotients of Unbounded Parallelism

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Theoretical Aspects of Computing - ICTAC 2015 (ICTAC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9399))

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Abstract

This is a language-theoretic investigation into a situation where a server serves an unbounded number of requests, and handling a request requires a bounded number of (arbitrarily delayed) steps. From a description of the system in interleaving semantics, one endeavours to determine whether some sequence from a given regular language is possible. We model unbounded parallelism using the iterated shuffle operator, investigate quotients of the so-called simple shuffled languages with regular languages, and prove a sufficient condition for obtaining another simple shuffled language by that operation.

N.E. Flick—This work is supported by the German Research Foundation (DFG), grant GRK 1765 (Research Training Group – System Correctness under Adverse Conditions).

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Notes

  1. 1.

    The dots indicate that the transition system may have further structure, such as initial states or labels. This notation stems from [10].

  2. 2.

    The order of the \(P'\) letters in \(A^-(t)\) could just as well be fixed, but \(\psi ^{-1}\) is required so the P letters can appear wherever they are needed.

  3. 3.

    Equivalently described in [12] as a “Vector Addition System with States” (VASS).

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Acknowledgements

We would like to thank the anonymous reviewers for providing valuable comments.

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Authors and Affiliations

  1. Carl von Ossietzky Universität, 26111, Oldenburg, Germany

    Nils Erik Flick

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  1. Nils Erik Flick
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Correspondence to Nils Erik Flick .

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Editors and Affiliations

  1. University of Lübeck, Lübeck, Schleswig-Holstein, Germany

    Martin Leucker

  2. Pontificia Universidad Javeriana-Cali, Cali, Colombia

    Camilo Rueda

  3. Pontificia Universidad Javeriana-Cali, CNRS LIX École Polytechnique de Paris, Palaiseau Cedex, France

    Frank D. Valencia

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Flick, N.E. (2015). Quotients of Unbounded Parallelism. In: Leucker, M., Rueda, C., Valencia, F. (eds) Theoretical Aspects of Computing - ICTAC 2015. ICTAC 2015. Lecture Notes in Computer Science(), vol 9399. Springer, Cham. https://doi.org/10.1007/978-3-319-25150-9_15

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  • DOI: https://doi.org/10.1007/978-3-319-25150-9_15

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  • Online ISBN: 978-3-319-25150-9

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