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CSR
2008
Springer

The Most General Conservation Law for a Cellular Automaton

9 years 1 months ago
The Most General Conservation Law for a Cellular Automaton
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.
Enrico Formenti, Jarkko Kari, Siamak Taati
Added 19 Oct 2010
Updated 19 Oct 2010
Type Conference
Year 2008
Where CSR
Authors Enrico Formenti, Jarkko Kari, Siamak Taati
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