On the computational power of totalistic cellular automata

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Totalistic cellular automata, introduced by S. Wolfram, are cellular automata in which the state transition function depends only on the sum of the states in a cell's neighborhood. Each state is considered as a nonnegative integer and the sum includes the cell's own state. It is shown that one-dimensional totalistic cellular automata can simulate an arbitrary Turing machine in linear time, even when the neighborhood is restricted to one cell on each side. This result settles Wolfram's conjecture that totalistic cellular automata are computation-universal.

Original languageEnglish
Pages (from-to)43-52
Number of pages10
JournalMathematical Systems Theory
Issue number1
StatePublished - Dec 1987

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Mathematics
  • Computational Theory and Mathematics


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