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

  • David Harel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 158)


In recent years many diverse logical systems for reasoning about programs have been shown to posses a highly undecidable, viz Π 1 1 -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 1 1 -complete.

It is hoped that the paper, which contains also NP-, PSPACE-, Π 1 0 - and Π 2 0 -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".


Temporal Logic Turing Machine Propositional Calculus Atomic Formula Linear Temporal Logic 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • David Harel
    • 1
  1. 1.Department of Applied MathematicsThe Weizmann Institute of ScienceRehovotISRAEL

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