Reliable Cellular Automata with Self-Organization
<|reference_start|>Reliable Cellular Automata with Self-Organization: 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 the initial configuration does not have to encode an infinite hierarchy -- this will be built up over time.   This is a corrected and strengthened version of the journal paper of 2001.<|reference_end|>
@article{gacs2000reliable,
    title={Reliable Cellular Automata with Self-Organization},
    author={Peter Gacs},
    journal={J. of Stat. Phys. vol.103 (2001), no. 1/2, 45-267},
    year={2000},
    doi={10.1023/A:1004823720305},
    archivePrefix={arXiv},
    eprint={math/0003117},
    primaryClass={math.PR cs.DC}
}