Theory of Computing Systems

, Volume 30, Issue 2, pp 145–163 | Cite as

Wang tilings and distributed verification on anonymous torus networks

  • V. R. Syrotiuk
  • C. J. Colbourn
  • J. Pachl
Article
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Abstract

Considern 2 processors arranged in ann × n torus network in which each processor is connected by direct communication channels with its four neighbours. This paper studies the followingverification problem on anonymousn × n torus networks: verify whether the network is oriented; that is, verify whether there is an agreement, among all processors, on a consistent channel labelling. The problem is to be solved by a distributed algorithm executed by the processors themselves.

If processors can label their channels arbitrarily, then there are network labellings that are not oriented but, to the processors, are indistinguishable from ones that are oriented. Hence there is no deterministic distributed verification algorithm. However, a verification algorithm does exist if the initial labellings are suitably restricted. We describe the restrictions placed on the initial labellings by subsets of the permutation groupS 4.

We show that the existence of an algorithm for verification is equivalent to the existence of certain tilings of the torus with Wang tiles. Using this equivalence, we have determined the existence of a distributed algorithm for the verification problem for alln × n torus networks for an important class of restrictions, the subgroups ofS 4.

Keywords

Orientation Model Finite Automaton Verification Algorithm Verification Problem Initial Labellings 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag New York Inc 1997

Authors and Affiliations

  • V. R. Syrotiuk
    • 1
  • C. J. Colbourn
    • 2
  • J. Pachl
    • 3
  1. 1.Computer Science Program, Mail Station EC 3.1University of Texas at DallasRichardsonUSA
  2. 2.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  3. 3.Department of Computer ScienceUniversity of WaterlooWaterlooCanada

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