no. 3
Number-conserving reversible cellular automata and their computation-universality
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) no. 3, pp. 239-258

We introduce a new model of cellular automaton called a one-dimensional number-conserving partitioned cellular automaton (NC-PCA). An NC-PCA is a system such that a state of a cell is represented by a triple of non-negative integers, and the total (i.e., sum) of integers over the configuration is conserved throughout its evolving (computing) process. It can be thought as a kind of modelization of the physical conservation law of mass (particles) or energy. We also define a reversible version of NC-PCA, and prove that a reversible NC-PCA is computation-universal. It is proved by showing that a reversible two-counter machine, which has been known to be universal, can be simulated by a reversible NC-PCA.

Classification : 68Q80, 68Q05
Keywords: cellular automata, reversibility, conservation law, universality 
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     author = {Morita, Kenichi and Imai, Katsunobu},
     title = {Number-conserving reversible cellular automata and their computation-universality},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {239--258},
     year = {2001},
     publisher = {EDP Sciences},
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Morita, Kenichi; Imai, Katsunobu. Number-conserving reversible cellular automata and their computation-universality. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) no. 3, pp. 239-258. https://www.numdam.org/item/ITA_2001__35_3_239_0/

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