Reversibility of Elementary Cellular Automata under Fully Asynchronous Update

A Guided Tour of Asynchronous Cellular Automata

“…Another point of view considered the case of fully asynchronous updating: as the evolution of the system is adequately described by a Markov chain, reversibility is identified with the property of recurrence of this chain [116]. A classification of the ECA rules into three classes was then proposed based on this tool: (a) The recurrent rules are those which make the system always return to its initial condition.…”

Asynchronous Cellular Automata

“…Another approach has been proposed by Sethi et al: to interpret the reversibility of a system as the possibility to always back to the initial condition [SFD14]. The problem then amounts to deciding the recurrence property of the Markov chain.…”

Asynchronous cellular automata and pattern classification

“…Note that each state of figure 1 converges to a fixed point. During the evolution of an ACA, a sequence (u t ) t∈N of cells can be observed where u t denotes the cell updated at time t. We call the sequence as update pattern [45]. For an initial condition x and an update pattern U , the evolution of the system is given by the sequence of states (x t ) obtained by successive applications of the updates of U .…”

“…In this section, we report the method of finding the average convergence time of ACA. In our earlier work [46], we have experimentally studied the convergence time of ACAs. We have simulated ACA rules to find their average convergence time and studied the rate of growth of convergence time with respect to the size of automaton.…”