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Reversible Cellular Automata in Presence of Noise Rapidly Forget Everything (Invited Talk)

Author Siamak Taati

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Siamak Taati
  • Department of Mathematics, American University of Beirut, Lebanon

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Siamak Taati. Reversible Cellular Automata in Presence of Noise Rapidly Forget Everything (Invited Talk). In 27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021). Open Access Series in Informatics (OASIcs), Volume 90, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/OASIcs.AUTOMATA.2021.3

Abstract

We consider reversible and surjective cellular automata perturbed with noise. We show that, in the presence of positive additive noise, the cellular automaton forgets all the information regarding its initial configuration exponentially fast. In particular, the state of a finite collection of cells with diameter n becomes indistinguishable from pure noise after O(log n) time steps. This highlights the seemingly unavoidable need for irreversibility in order to perform scalable reliable computation in the presence of noise.

Subject Classification

ACM Subject Classification
  • Hardware → Reversible logic
  • Hardware → Fault tolerance
  • Theory of computation → Parallel computing models
  • Mathematics of computing → Stochastic processes
  • Mathematics of computing → Information theory
Keywords
  • Reversible cellular automata
  • surjective cellular automata
  • noise
  • probabilistic cellular automata
  • ergodicity
  • entropy
  • reversible computing
  • reliable computing
  • fault tolerance

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