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Superposable Trellis Automata

  • Nicolas Reimen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 629)

Abstract

A property of superposability is defined here for Treillis Automata as an equivalent of the linearity property of Cellular Automata. We take advantage of the binary local transition function of TAs, which enables us to use an infix notation for it, to study this property in an algebraic framework. We show that a TA is superposable iff its local transition function operates on its set of states as a commutative monoid law and that the general case of commutative monoids is reducible to the case of Abelian groups in which the space-time diagrams obtained are isomorphic to a superposition of figures representing the triangle of binomial coefficients (Pascal's triangle) modulo integers.

Keywords

Cellular Automaton Initial Configuration Neutral Element Binomial Coefficient Commutative Monoid 
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 Berlin Heidelberg 1992

Authors and Affiliations

  • Nicolas Reimen
    • 1
  1. 1.Institut Blaise PascalLITPParis

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