On conservative and monotone one-dimensional cellular automata and their particle representation

  • Authors:

  • Andrés Moreira;Nino Boccara;Eric Goles

  • Affiliations:

  • Center for Mathematical Modeling and Departamento de Ingeniería Matemática FCFM, U. de Chile, Casilla 170/3-Correo 3, Santiago, Chile;Department of Physics, University of Illinois, Chicago and DRECAM/SPEC, CE Saclay, 91191 Gif-sur-Yvette Cedex, France;Center for Mathematical Modeling and Departamento de Ingeniería Matemática FCFM, U. de Chile, Casilla 170/3-Correo 3, Santiago, Chile

  • Venue:
  • Theoretical Computer Science - Special issue: Theoretical aspects of cellular automata
  • Year:
  • 2004

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Abstract

Number-conserving (or conservative) cellular automata (CA) have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several issues concerning one-dimensional cellular automata which are conservative, monotone (specially "non-increasing"), or that allow a weaker kind of conservative dynamics. We introduce a formalism of "particle automata", and discuss several properties that they may exhibit, some of which, like anticipation and momentum preservation, happen to be intrinsic to the conservative CA they represent. For monotone CA we give a characterization, and then show that they too are equivalent to the corresponding class of particle automata. Finally, we show how to determine, for a given CA and a given integer b, whether its states admit a b-neighborhood-dependent relabeling whose sum is conserved by the CA iteration; this can be used to uncover conservative principles and particle-like behavior underlying the dynamics of some CA. Compliments at http://www.dim.uchile.cl/~anmoreir/ncca