Abstract
A number-conserving cellular automaton (NCCA) is a cellular automaton whose states are integers and whose transition function keeps the sum of all cells constant throughout its evolution. It can be seen as a kind of modeling of the physical conservation laws of mass or energy. In this paper we show a construction method of radius 1/2 NCCAs. The local transition function is expressed via a single unary function which can be regarded as ‘flows’ of numbers. In spite of the strong constraint, we constructed radius 1/2 NCCAs that simulate any radius 1/2 cellular automata or any radius 1 NCCA. We also consider the state complexity of these non-splitting simulations (4n 2 + 2n + 1 and 8n 2 + 12n − 16, respectively). These results also imply existence of an intrinsically universal radius 1/2 NCCA.
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Imai, K., Alhazov, A. (2010). On Universality of Radius 1/2 Number-Conserving Cellular Automata. In: Calude, C.S., Hagiya, M., Morita, K., Rozenberg, G., Timmis, J. (eds) Unconventional Computation. UC 2010. Lecture Notes in Computer Science, vol 6079. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13523-1_8
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DOI: https://doi.org/10.1007/978-3-642-13523-1_8
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