Gacs, Peter2018-06-142018-06-142001-04-01P Gacs. 2001. "Reliable cellular automata with self-organization." Journal of Statistical Physics, Volume 103, Issue 1-2, pp. 45 - 267 (223).0022-47151572-9613https://hdl.handle.net/2144/29390In 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.p. 45 - 267Science & technologyPhysical sciencesPhysics, mathematicalPhysicsProbabilistic cellular automataInteracting particle systemsRenormalizationErgodicityReliabilityFault-toleranceError-correctionSimulationHierarchySelf-organizationInteracting particle systemsMathematical sciencesFluids & plasmasArticle10.1023/A:1004823720305