Universality of One-Dimensional Reversible and Number-Conserving Cellular Automata

Autor:	Morita, Kenichi
Rok vydání:	2012
Předmět:	Computer Science - Formal Languages and Automata Theory Computer Science - Computational Complexity Computer Science - Discrete Mathematics Nonlinear Sciences - Cellular Automata and Lattice Gases F.1.1 F.1.2 F.1.3
Zdroj:	EPTCS 90, 2012, pp. 142-150
Druh dokumentu:	Working Paper
DOI:	10.4204/EPTCS.90.12
Popis:	We study one-dimensional reversible and number-conserving cellular automata (RNCCA) that have both properties of reversibility and number-conservation. In the case of 2-neighbor RNCCA, Garc\'ia-Ramos proved that every RNCCA shows trivial behavior in the sense that all the signals in the RNCCA do not interact each other. However, if we increase the neighborhood size, we can find many complex RNCCAs. Here, we show that for any one-dimensional 2-neighbor reversible partitioned CA (RPCA) with s states, we can construct a 4-neighbor RNCCA with 4s states that simulates the former. Since it is known that there is a computationally universal 24-state 2-neighbor RPCA, we obtain a universal 96-state 4-neighbor RNCCA. Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.2498
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1208.2760 Zobrazit plný text záznamu View this record from Arxiv