Nonlinear Sciences – Cellular Automata and Lattice Gases
Scientific paper
2010-12-03
Nonlinear Sciences
Cellular Automata and Lattice Gases
Journ\'ees Automates Cellulaires 2010, Turku : Finland (2010)
Scientific paper
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.
Capobianco Silvio
Uustalu Tarmo
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