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Number Conservation Property of Binary Cellular Automata Under α-Asynchronous Update
Raju Hazari and Sukanta Das

This paper studies the number conservation behavior of binary asynchronous cellular automata (ACAs). We consider here α-asynchronous update scheme. It is, however, shown in the beginning of the study that no binary CA (except identity rule), in general, can be claimed as number conserving under asynchronous update. We then introduce the idea of probabilistic number conservation of ACAs. We find a set of binary ACAs which are probabilistic number conserving ACAs. We observe that these ACAs are not dependent on any specific value of α. Further, some additional ACAs have been found which have a tendency to conserve the expected number of 1s of the seeds having density 0.5.

Keywords: Cellular automata (CAs), asynchronous update, probabilistic number conserving CAs, rule min term (RMT), density sensitivity.

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