A Categorical Outlook on Cellular Automata
Cellular Automata and Lattice Gases
2010-12-07 v1 Logic in Computer Science
Category Theory
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.
Keywords
Cite
@article{arxiv.1012.1220,
title = {A Categorical Outlook on Cellular Automata},
author = {Silvio Capobianco and Tarmo Uustalu},
journal= {arXiv preprint arXiv:1012.1220},
year = {2010}
}
Comments
Journ\'ees Automates Cellulaires 2010, Turku : Finland (2010)