2012•Electronic Proceedings in Theoretical Computer ScienceOpen access

Phase Space Invertible Asynchronous Cellular Automata

Simon Wacker, Thomas Worsch

Abstract

While for synchronous deterministic cellular automata there is an accepted definition of reversibility, the situation is less clear for asynchronous cellular automata. We first discuss a few possibilities and then investigate what we call phase space invertible asynchronous cellular automata in more detail. We will show that for each Turing machine there is such a cellular automaton simulating it, and that it is decidable whether an asynchronous cellular automaton has this property or not, even in higher dimensions.

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Key concepts: Asynchronous cellular automaton, Cellular automaton, Mobile automaton, Reversible cellular automaton, Block cellular automaton, Stochastic cellular automaton, Asynchronous communication, Computer science