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A Categorical Outlook on Cellular Automata

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00542015
Contributor : Pierre Guillon <>
Submitted on : Wednesday, December 1, 2010 - 4:30:16 PM
Last modification on : Monday, December 6, 2010 - 12:51:06 PM
Long-term archiving on: : Wednesday, March 2, 2011 - 3:17:12 AM

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  • HAL Id : hal-00542015, version 1
  • ARXIV : 1012.1220

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Silvio Capobianco, Tarmo Uustalu. A Categorical Outlook on Cellular Automata. Journées Automates Cellulaires 2010, Dec 2010, Turku, Finland. pp.88-99. ⟨hal-00542015⟩

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