Concurrent Kleene Algebra with Observations: From Hypotheses to Completeness

Concurrent Kleene Algebra (CKA) extends basic Kleene algebra with a parallel composition operator, which enables reasoning about concurrent programs. However, CKA fundamentally misses tests, which are needed to model standard programming constructs such as conditionals and [Formula: see text] -loops...

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Autores principales: Kappé, Tobias, Brunet, Paul, Silva, Alexandra, Wagemaker, Jana, Zanasi, Fabio
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7788622/
http://dx.doi.org/10.1007/978-3-030-45231-5_20
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author Kappé, Tobias
Brunet, Paul
Silva, Alexandra
Wagemaker, Jana
Zanasi, Fabio
author_facet Kappé, Tobias
Brunet, Paul
Silva, Alexandra
Wagemaker, Jana
Zanasi, Fabio
author_sort Kappé, Tobias
collection PubMed
description Concurrent Kleene Algebra (CKA) extends basic Kleene algebra with a parallel composition operator, which enables reasoning about concurrent programs. However, CKA fundamentally misses tests, which are needed to model standard programming constructs such as conditionals and [Formula: see text] -loops. It turns out that integrating tests in CKA is subtle, due to their interaction with parallelism. In this paper we provide a solution in the form of Concurrent Kleene Algebra with Observations (CKAO). Our main contribution is a completeness theorem for CKAO. Our result resorts on a more general study of CKA “with hypotheses”, of which CKAO turns out to be an instance: this analysis is of independent interest, as it can be applied to extensions of CKA other than CKAO.
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spelling pubmed-77886222021-01-07 Concurrent Kleene Algebra with Observations: From Hypotheses to Completeness Kappé, Tobias Brunet, Paul Silva, Alexandra Wagemaker, Jana Zanasi, Fabio Foundations of Software Science and Computation Structures Article Concurrent Kleene Algebra (CKA) extends basic Kleene algebra with a parallel composition operator, which enables reasoning about concurrent programs. However, CKA fundamentally misses tests, which are needed to model standard programming constructs such as conditionals and [Formula: see text] -loops. It turns out that integrating tests in CKA is subtle, due to their interaction with parallelism. In this paper we provide a solution in the form of Concurrent Kleene Algebra with Observations (CKAO). Our main contribution is a completeness theorem for CKAO. Our result resorts on a more general study of CKA “with hypotheses”, of which CKAO turns out to be an instance: this analysis is of independent interest, as it can be applied to extensions of CKA other than CKAO. 2020-04-17 /pmc/articles/PMC7788622/ http://dx.doi.org/10.1007/978-3-030-45231-5_20 Text en © The Author(s) 2020 Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
spellingShingle Article
Kappé, Tobias
Brunet, Paul
Silva, Alexandra
Wagemaker, Jana
Zanasi, Fabio
Concurrent Kleene Algebra with Observations: From Hypotheses to Completeness
title Concurrent Kleene Algebra with Observations: From Hypotheses to Completeness
title_full Concurrent Kleene Algebra with Observations: From Hypotheses to Completeness
title_fullStr Concurrent Kleene Algebra with Observations: From Hypotheses to Completeness
title_full_unstemmed Concurrent Kleene Algebra with Observations: From Hypotheses to Completeness
title_short Concurrent Kleene Algebra with Observations: From Hypotheses to Completeness
title_sort concurrent kleene algebra with observations: from hypotheses to completeness
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7788622/
http://dx.doi.org/10.1007/978-3-030-45231-5_20
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