Abstract
We study the group-valued and semigroup-valued conservation laws in cellular automata (CA). We provide examples to distinguish between semigroup-valued, group-valued and real-valued conservation laws. We prove that, even in one-dimensional case, it is undecidable if a CA has any non-trivial conservation law of each type. For a fixed range, each CA has a most general (group-valued or semigroup-valued) conservation law, encapsulating all conservation laws of that range. For one-dimensional CA the semigroup corresponding to such a most general conservation law has an effectively constructible finite presentation, while for higher-dimensional ones no such effective construction exists. © 2008 Springer-Verlag Berlin Heidelberg.
Cite
CITATION STYLE
Formenti, E., Kari, J., & Taati, S. (2008). The most general conservation law for a cellular automaton. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5010 LNCS, pp. 194–203). https://doi.org/10.1007/978-3-540-79709-8_21
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