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| HAL: hal-00542015, version 1 |
| arXiv: 1012.1220 |
| Detailed view |  Export this paper |
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| Journées Automates Cellulaires 2010, Turku : Finland (2010) |
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| A Categorical Outlook on Cellular Automata |
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| Silvio Capobianco 1Tarmo Uustalu 1 |
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| (2010-12-15) |
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| 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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| 1: | Institute of Cybernetics [Tallinn] |
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Tallinn Technical University |
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| Subject | : | Computer Science/Other |
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| cellular automata – context-dependent computation – comonads |
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| hal-00542015, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00542015 | |
| oai:hal.archives-ouvertes.fr:hal-00542015 | |
| From: Pierre Guillon | |
| Submitted on: Wednesday, 1 December 2010 16:30:16 | |
| Updated on: Monday, 6 December 2010 12:51:06 | |
