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On the Termination Problem for Counter Machines with Incrementing Errors

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Book cover Reachability Problems (RP 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11674))

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Abstract

In contrast to their reliable and lossy-error counterparts whose termination problems are either undecidable or non-primitive recursive, the termination problem for counter machines with incrementing errors is shown to be PSpace-hard but remains solvable in ExpSpace. This is a notable decrease in complexity over that of insertion-error channel systems (with emptiness testing) whose termination problem is known to be non-elementary. Furthermore, by fixing the number of available counters, we obtain a tight NLogSpace-complete bound for the termination problem.

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Notes

  1. 1.

    It is incorrectly claimed in [7] that the satisfiability problem for this logic is non-elementary, erroneously stating that the termination problem for ICMs matches that of incrementing channel systems with emptiness testing, as refuted here in Theorem 3.2.

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Acknowledgements

I would like to thank the anonymous referees for their helpful and invaluable suggestions.

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Authors and Affiliations

  1. Department of Informatics, King’s College, London, UK

    Christopher Hampson

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  1. Christopher Hampson
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Correspondence to Christopher Hampson .

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Editors and Affiliations

  1. Université Libre de Bruxelles, Brussels, Belgium

    Emmanuel Filiot

  2. Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    Raphaël Jungers

  3. University of Liverpool, Liverpool, UK

    Igor Potapov

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Hampson, C. (2019). On the Termination Problem for Counter Machines with Incrementing Errors. In: Filiot, E., Jungers, R., Potapov, I. (eds) Reachability Problems. RP 2019. Lecture Notes in Computer Science(), vol 11674. Springer, Cham. https://doi.org/10.1007/978-3-030-30806-3_11

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  • DOI: https://doi.org/10.1007/978-3-030-30806-3_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-30805-6

  • Online ISBN: 978-3-030-30806-3

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