Reliable cellular automata with self-organization.

*(English)*Zbl 0973.68158Summary: 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 I 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.

##### MSC:

68Q80 | Cellular automata (computational aspects) |

82C20 | Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics |

37B15 | Dynamical aspects of cellular automata |

82C26 | Dynamic and nonequilibrium phase transitions (general) in statistical mechanics |