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Documents authored by Wagemaker, Jana

Document
DOI: 10.4230/LIPIcs.CONCUR.2022.26
Completeness Theorems for Kleene Algebra with Top

Authors: Damien Pous and Jana Wagemaker

Published in: LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

Abstract
We prove two completeness results for Kleene algebra with a top element, with respect to languages and binary relations. While the equational theories of those two classes of models coincide over the signature of Kleene algebra, this is no longer the case when we consider an additional constant "top" for the full element. Indeed, the full relation satisfies more laws than the full language, and we show that those additional laws can all be derived from a single additional axiom. We recover that the two equational theories coincide if we slightly generalise the notion of relational model, allowing sub-algebras of relations where top is a greatest element but not necessarily the full relation. We use models of closed languages and reductions in order to prove our completeness results, which are relative to any axiomatisation of the algebra of regular events.
Cite as

Damien Pous and Jana Wagemaker. Completeness Theorems for Kleene Algebra with Top. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{pous_et_al:LIPIcs.CONCUR.2022.26,
  author =	{Pous, Damien and Wagemaker, Jana},
  title =	{{Completeness Theorems for Kleene Algebra with Top}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{26:1--26:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2022.26},
  URN =		{urn:nbn:de:0030-drops-170890},
  doi =		{10.4230/LIPIcs.CONCUR.2022.26},
  annote =	{Keywords: Kleene algebra, Hypotheses, Completeness, Closed languages}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2020.20
Partially Observable Concurrent Kleene Algebra

Authors: Jana Wagemaker, Paul Brunet, Simon Docherty, Tobias Kappé, Jurriaan Rot, and Alexandra Silva

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

Abstract
We introduce partially observable concurrent Kleene algebra (POCKA), an algebraic framework to reason about concurrent programs with variables as well as control structures, such as conditionals and loops, that depend on those variables. We illustrate the use of POCKA through concrete examples. We prove that POCKA is a sound and complete axiomatisation of a model of partial observations, and show the semantics passes an important check for sequential consistency.
Cite as

Jana Wagemaker, Paul Brunet, Simon Docherty, Tobias Kappé, Jurriaan Rot, and Alexandra Silva. Partially Observable Concurrent Kleene Algebra. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{wagemaker_et_al:LIPIcs.CONCUR.2020.20,
  author =	{Wagemaker, Jana and Brunet, Paul and Docherty, Simon and Kapp\'{e}, Tobias and Rot, Jurriaan and Silva, Alexandra},
  title =	{{Partially Observable Concurrent Kleene Algebra}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{20:1--20:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.20},
  URN =		{urn:nbn:de:0030-drops-128324},
  doi =		{10.4230/LIPIcs.CONCUR.2020.20},
  annote =	{Keywords: Concurrent Kleene algebra, Kleene algebra with tests, observations, axiomatisation, completeness, sequential consistency}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2019.41
Kleene Algebra with Observations

Authors: Tobias Kappé, Paul Brunet, Jurriaan Rot, Alexandra Silva, Jana Wagemaker, and Fabio Zanasi

Published in: LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)

Abstract
Kleene algebra with tests (KAT) is an algebraic framework for reasoning about the control flow of sequential programs. Generalising KAT to reason about concurrent programs is not straightforward, because axioms native to KAT in conjunction with expected axioms for concurrency lead to an anomalous equation. In this paper, we propose Kleene algebra with observations (KAO), a variant of KAT, as an alternative foundation for extending KAT to a concurrent setting. We characterise the free model of KAO, and establish a decision procedure w.r.t. its equational theory.
Cite as

Tobias Kappé, Paul Brunet, Jurriaan Rot, Alexandra Silva, Jana Wagemaker, and Fabio Zanasi. Kleene Algebra with Observations. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 41:1-41:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{kappe_et_al:LIPIcs.CONCUR.2019.41,
  author =	{Kapp\'{e}, Tobias and Brunet, Paul and Rot, Jurriaan and Silva, Alexandra and Wagemaker, Jana and Zanasi, Fabio},
  title =	{{Kleene Algebra with Observations}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{41:1--41:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Fokkink, Wan and van Glabbeek, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.41},
  URN =		{urn:nbn:de:0030-drops-109431},
  doi =		{10.4230/LIPIcs.CONCUR.2019.41},
  annote =	{Keywords: Concurrent Kleene algebra, Kleene algebra with tests, free model, axiomatisation, decision procedure}
}
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