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Recurring dominoes: Making the highly undecidable highly understandable (preliminary report)

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Foundations of Computation Theory (FCT 1983)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 158))

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Abstract

In recent years many diverse logical systems for reasoning about programs have been shown to posses a highly undecidable, viz Π 11 -complete, validity problem. All such known results are reproved in this paper in a uniform and transparent manner by reductions from recurring domino problems. These are simple variants of the classical unbounded domino (or tiling) problems introduced by Wang and the bounded versions defined by Lewis. While the former are (weakly) undecidable and the latter complete in various complexity classes, the problems in the new class are Σ 11 -complete.

It is hoped that the paper, which contains also NP-, PSPACE-, Π 01 - and Π 02 -hardness results for logical systems, will enhance interest in the appealing medium of domino problems as a useful set of reduction tools for exhibiting "bad behavior".

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Authors and Affiliations

  1. Department of Applied Mathematics, The Weizmann Institute of Science, 76100, Rehovot, ISRAEL

    David Harel

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  1. David Harel
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Marek Karpinski

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© 1983 Springer-Verlag Berlin Heidelberg

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Harel, D. (1983). Recurring dominoes: Making the highly undecidable highly understandable (preliminary report). In: Karpinski, M. (eds) Foundations of Computation Theory. FCT 1983. Lecture Notes in Computer Science, vol 158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12689-9_103

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  • DOI: https://doi.org/10.1007/3-540-12689-9_103

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12689-8

  • Online ISBN: 978-3-540-38682-7

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