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A Dialectica-Like Interpretation of a Linear MSO on Infinite Words

Cécilia Pradic Orcid Logo, Colin Riba

Lecture Notes in Computer Science, Volume: 11425, Pages: 470 - 487

Swansea University Author: Cécilia Pradic Orcid Logo

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DOI (Published version): 10.1007/978-3-030-17127-8_27

Abstract

We devise a variant of Dialectica interpretation of intuitionistic linear logic for Open image in new window, a linear logic-based version MSO over infinite words. Open image in new window was known to be correct and complete w.r.t. Church’s synthesis, thanks to an automata-based realizability model...

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Published in: Lecture Notes in Computer Science
ISSN: 0302-9743 1611-3349
Published: Cham Springer International Publishing 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa58114
first_indexed 2021-10-15T15:59:26Z
last_indexed 2021-10-19T03:23:09Z
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spelling 2021-10-18T13:22:01.0514049 v2 58114 2021-09-27 A Dialectica-Like Interpretation of a Linear MSO on Infinite Words 3b6e9ebd791c875dac266b3b0b358a58 0000-0002-1600-8846 Cécilia Pradic Cécilia Pradic true false 2021-09-27 MACS We devise a variant of Dialectica interpretation of intuitionistic linear logic for Open image in new window, a linear logic-based version MSO over infinite words. Open image in new window was known to be correct and complete w.r.t. Church’s synthesis, thanks to an automata-based realizability model. Invoking Büchi-Landweber Theorem and building on a complete axiomatization of MSO on infinite words, our interpretation provides us with a syntactic approach, without any further construction of automata on infinite words. Via Dialectica, as linear negation directly corresponds to switching players in games, we furthermore obtain a complete logic: either a closed formula or its linear negation is provable. This completely axiomatizes the theory of the realizability model of Open image in new window. Besides, this shows that in principle, one can solve Church’s synthesis for a given ∀∃ -formula by only looking for proofs of either that formula or its linear negation. Conference Paper/Proceeding/Abstract Lecture Notes in Computer Science 11425 470 487 Springer International Publishing Cham 0302-9743 1611-3349 5 4 2019 2019-04-05 10.1007/978-3-030-17127-8_27 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2021-10-18T13:22:01.0514049 2021-09-27T22:57:32.3261199 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Cécilia Pradic 0000-0002-1600-8846 1 Colin Riba 2
title A Dialectica-Like Interpretation of a Linear MSO on Infinite Words
spellingShingle A Dialectica-Like Interpretation of a Linear MSO on Infinite Words
Cécilia Pradic
title_short A Dialectica-Like Interpretation of a Linear MSO on Infinite Words
title_full A Dialectica-Like Interpretation of a Linear MSO on Infinite Words
title_fullStr A Dialectica-Like Interpretation of a Linear MSO on Infinite Words
title_full_unstemmed A Dialectica-Like Interpretation of a Linear MSO on Infinite Words
title_sort A Dialectica-Like Interpretation of a Linear MSO on Infinite Words
author_id_str_mv 3b6e9ebd791c875dac266b3b0b358a58
author_id_fullname_str_mv 3b6e9ebd791c875dac266b3b0b358a58_***_Cécilia Pradic
author Cécilia Pradic
author2 Cécilia Pradic
Colin Riba
format Conference Paper/Proceeding/Abstract
container_title Lecture Notes in Computer Science
container_volume 11425
container_start_page 470
publishDate 2019
institution Swansea University
issn 0302-9743
1611-3349
doi_str_mv 10.1007/978-3-030-17127-8_27
publisher Springer International Publishing
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
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description We devise a variant of Dialectica interpretation of intuitionistic linear logic for Open image in new window, a linear logic-based version MSO over infinite words. Open image in new window was known to be correct and complete w.r.t. Church’s synthesis, thanks to an automata-based realizability model. Invoking Büchi-Landweber Theorem and building on a complete axiomatization of MSO on infinite words, our interpretation provides us with a syntactic approach, without any further construction of automata on infinite words. Via Dialectica, as linear negation directly corresponds to switching players in games, we furthermore obtain a complete logic: either a closed formula or its linear negation is provable. This completely axiomatizes the theory of the realizability model of Open image in new window. Besides, this shows that in principle, one can solve Church’s synthesis for a given ∀∃ -formula by only looking for proofs of either that formula or its linear negation.
published_date 2019-04-05T16:34:31Z
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