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Journal of Statistical Physics

, Volume 103, Issue 1–2, pp 45–267 | Cite as

Reliable Cellular Automata with Self-Organization

  • Peter Gács
Article

Abstract

In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2 dimensions, and this solution can be used to construct a simple 3-dimensional discrete-time universal fault-tolerant cellular automaton. This technique does not help much to solve the following problems: remembering a bit of information in 1 dimension; computing in dimensions lower than 3; computing in any dimension with non-synchronized transitions. Our more complex technique organizes the cells in blocks that perform a reliable simulation of a second (generalized) cellular automaton. The cells of the latter automaton are also organized in blocks, simulating even more reliably a third automaton, etc. Since all this (a possibly infinite hierarchy) is organized in “software,” it must be under repair all the time from damage caused by errors. A large part of the problem is essentially self-stabilization recovering from a mess of arbitrary size and content. The present paper constructs an asynchronous one-dimensional fault-tolerant cellular automaton, with the further feature of “self-organization.” The latter means that unless a large amount of input information must be given, the initial configuration can be chosen homogeneous.

probabilistic cellular automata interacting particle systems renormalization ergodicity reliability fault-tolerance error-correction simulation hierarchy self-organization 

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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • Peter Gács
    • 1
  1. 1.Computer Science DepartmentBoston UniversityBoston

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