Programming and Computer Software

, Volume 32, Issue 2, pp 84–89 | Cite as

Discrete relations on abstract simplicial complexes

  • V. V. Kornyak


On the one hand, a system of discrete relations is a generalization of cellular automaton and, on the other hand, it is a set-theoretical analog of a system of polynomial equations. An approach to studying such systems that is based on set-theoretical and topological constructs is considered. The proposed approach is implemented as a C program. Results of application of this approach to some binary cellular automata are given. In the binary case, cellular automata can be represented by systems of polynomial equations, which are normally studied by the Gröbner basis method. Our approach is compared with this method on some examples.


Operating System Artificial Intelligence Software Engineer Cellular Automaton Basis Method 
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  1. 1.
    Lidl, R. and Niederreiter, H., Finite Fields, Reading, Mass.: Addison-Wesley, 1983.Google Scholar
  2. 2.
    Hilton, P. and Wayle, S., Homology Theory: An Introduction to Algebraic Topology, Cambridge Univ. Press, 1960.Google Scholar
  3. 3.
    ’t Hooft, G., Dimensional Reduction in Quantum Gravity (Essay Dedicated to Abdus Salam), Utrecht preprint THU-93/26, 1993, p. 13.
  4. 4.
    Wolfram, S., A New Kind of Science, Wolfram Media, 2002.Google Scholar
  5. 5.

Copyright information

© Pleiades Publishing, Inc. 2006

Authors and Affiliations

  • V. V. Kornyak
    • 1
  1. 1.Laboratory of Computer Science and AutomationJoint Institute for Nuclear ResearchDubna, Moscow oblastRussia

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