A Categorical Outlook on Cellular Automata

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A Categorical Outlook on Cellular Automata
In programming language semantics, it has proved to be fruitful to analyze context-dependent notions of computation, e.g., dataflow computation and attribute grammars, using comonads. We explore the viability and value of similar modeling of cellular automata. We identify local behaviors of cellular automata with coKleisli maps of the exponent comonad on the category of uniform spaces and uniformly continuous functions and exploit this equivalence to conclude some standard results about cellular automata as instances of basic category-theoretic generalities. In particular, we recover Ceccherini-Silberstein and Coornaert's version of the Curtis-Hedlund theorem.
Silvio Capobianco, Tarmo Uustalu
Added 01 Mar 2011
Updated 01 Mar 2011
Type Journal
Year 2010
Where CORR
Authors Silvio Capobianco, Tarmo Uustalu
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