Corpus ID: 2970397

Universality in Elementary Cellular Automata

@article{Cook2004UniversalityIE,
  title={Universality in Elementary Cellular Automata},
  author={Matthew Cook},
  journal={Complex Syst.},
  year={2004},
  volume={15}
}
  • Matthew Cook
  • Published 2004
  • Mathematics, Computer Science
  • Complex Syst.
The purpose of this paper is to prove that one of the simplest one dimensional cellular automata is computationally universal, implying that many questions concerning its behavior, such as whether a particular sequence of bits will occur, or whether the behavior will become periodic, are formally undecidable. The cellular automaton we will prove this for is known as “Rule 110” according to Wolfram’s numbering scheme [2]. Being a one dimensional cellular automaton, it consists of an infinitely… Expand
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References

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Universality and complexity in cellular automata
TLDR
Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes, and one class is probably capable of universal computation, so that properties of its infinite time behaviour are undecidable. Expand
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Thanks to David Eppstein for figuring out that the two-symbol machine can be achieved with only seven states
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Nordahl exhibited a universal one dimensional cellular automaton with (k ( 7, r ( 1) and (k ( 4, r ( 2), in Universal Computation in Simple One-Dimensional
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Stephen Wolfram notes that some simple cellular automata are " class 4 " , but does not yet notice any as simple as
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Stephen Wolfram notes that some simple cellular automata are "class 4", but does not yet notice any as simple as (k 2, r 1), in Undecidability and Intractibility in Theoretical Physics
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Winning ways for your mathematical plays
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