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Kleene Algebra with Hypotheses

Amina Doumane, Denis Kuperberg, Damien Pous, Cécilia Pradic Orcid Logo

Lecture Notes in Computer Science, Volume: 11425, Pages: 207 - 223

Swansea University Author: Cécilia Pradic Orcid Logo

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Abstract

We study the Horn theories of Kleene algebras and star continuous Kleene algebras, from the complexity point of view. While their equational theories coincide and are PSpace-complete, their Horn theories differ and are undecidable. We characterise the Horn theory of star continuous Kleene algebras i...

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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/cronfa58113
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spelling 2021-10-18T13:22:19.4650668 v2 58113 2021-09-27 Kleene Algebra with Hypotheses 3b6e9ebd791c875dac266b3b0b358a58 0000-0002-1600-8846 Cécilia Pradic Cécilia Pradic true false 2021-09-27 SCS We study the Horn theories of Kleene algebras and star continuous Kleene algebras, from the complexity point of view. While their equational theories coincide and are PSpace-complete, their Horn theories differ and are undecidable. We characterise the Horn theory of star continuous Kleene algebras in terms of downward closed languages and we show that when restricting the shape of allowed hypotheses, the problems lie in various levels of the arithmetical or analytical hierarchy. We also answer a question posed by Cohen about hypotheses of the form 1=S where S is a sum of letters: we show that it is decidable. Conference Paper/Proceeding/Abstract Lecture Notes in Computer Science 11425 207 223 Springer International Publishing Cham 0302-9743 1611-3349 Kleene algebra; Hypotheses; Horn theory; Complexity 5 4 2019 2019-04-05 10.1007/978-3-030-17127-8_12 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2021-10-18T13:22:19.4650668 2021-09-27T22:55:54.1690232 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Amina Doumane 1 Denis Kuperberg 2 Damien Pous 3 Cécilia Pradic 0000-0002-1600-8846 4 58113__21179__bb38b417353e4353bde053fc7ed16d0f.pdf 58113.pdf 2021-10-15T16:56:18.2230678 Output 393622 application/pdf Version of Record true © The Author(s) 2019. This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License true eng http://creativecommons.org/licenses/by/4.0/
title Kleene Algebra with Hypotheses
spellingShingle Kleene Algebra with Hypotheses
Cécilia Pradic
title_short Kleene Algebra with Hypotheses
title_full Kleene Algebra with Hypotheses
title_fullStr Kleene Algebra with Hypotheses
title_full_unstemmed Kleene Algebra with Hypotheses
title_sort Kleene Algebra with Hypotheses
author_id_str_mv 3b6e9ebd791c875dac266b3b0b358a58
author_id_fullname_str_mv 3b6e9ebd791c875dac266b3b0b358a58_***_Cécilia Pradic
author Cécilia Pradic
author2 Amina Doumane
Denis Kuperberg
Damien Pous
Cécilia Pradic
format Conference Paper/Proceeding/Abstract
container_title Lecture Notes in Computer Science
container_volume 11425
container_start_page 207
publishDate 2019
institution Swansea University
issn 0302-9743
1611-3349
doi_str_mv 10.1007/978-3-030-17127-8_12
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 study the Horn theories of Kleene algebras and star continuous Kleene algebras, from the complexity point of view. While their equational theories coincide and are PSpace-complete, their Horn theories differ and are undecidable. We characterise the Horn theory of star continuous Kleene algebras in terms of downward closed languages and we show that when restricting the shape of allowed hypotheses, the problems lie in various levels of the arithmetical or analytical hierarchy. We also answer a question posed by Cohen about hypotheses of the form 1=S where S is a sum of letters: we show that it is decidable.
published_date 2019-04-05T04:14:22Z
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score 10.997137