Comparing 1D and 2D Real Time on Cellular Automata

Authors Anaël Grandjean, Victor Poupet

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Anaël Grandjean
Victor Poupet

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Anaël Grandjean and Victor Poupet. Comparing 1D and 2D Real Time on Cellular Automata. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 367-378, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


We study the influence of the dimension of cellular automata (CA) for real time language recognition of one-dimensional languages with parallel input. Specifically, we focus on the question of determining whether every language that can be recognized in real time on a 2-dimensional CA working on the Moore neighborhood can also be recognized in real time by a 1-dimensional CA working on the standard two-way neighborhood. We show that 2-dimensional CA in real time can perform a linear number of simulations of a 1-dimensional real time CA. If the two classes are equal then the number of simulated instances can be polynomial.
  • Cellular automata
  • real time
  • language recognition


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