License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TLCA.2015.302
URN: urn:nbn:de:0030-drops-51719
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5171/
Riba, Colin
Fibrations of Tree Automata
Abstract
We propose a notion of morphisms between tree automata based on game semantics. Morphisms are winning strategies on a synchronous restriction of the linear implication between acceptance games. This leads to split indexed categories, with substitution based on a suitable notion of synchronous tree function. By restricting to tree functions issued from maps on alphabets, this gives a fibration of tree automata. We then discuss the (fibrewise) monoidal structure issued from the synchronous product of automata. We also discuss how a variant of the usual projection operation on automata leads to an existential quantification in the fibered sense. Our notion of morphism is correct (it respects language inclusion), and in a weaker sense also complete.
BibTeX - Entry
@InProceedings{riba:LIPIcs:2015:5171,
author = {Colin Riba},
title = {{Fibrations of Tree Automata}},
booktitle = {13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)},
pages = {302--316},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-87-3},
ISSN = {1868-8969},
year = {2015},
volume = {38},
editor = {Thorsten Altenkirch},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2015/5171},
URN = {urn:nbn:de:0030-drops-51719},
doi = {10.4230/LIPIcs.TLCA.2015.302},
annote = {Keywords: Tree automata, Game semantics, Categorical logic.}
}
Keywords: |
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Tree automata, Game semantics, Categorical logic. |
Collection: |
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13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015) |
Issue Date: |
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2015 |
Date of publication: |
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15.06.2015 |