2010/12/03 by Silvio Capobianco, Capobianco, Silvio, Tarmo Uustalu +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Category Theory (math.CT) #Cellular Automata and Applications #Cellular Automata and Lattice Gases (nlin.CG) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Logic in Computer Science (cs.LO) #Logic, programming, and type systems #cs.LO #math.CT #nlin.CG #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1012.1220
Journées Automates Cellulaires 2010, Turku : Finland (2010)
arxiv created 2010/12/03 · openalex publication_date 2010/12/03 · arxiv updated 2010/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.