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arXiv · 2002.09682

Concurrent Kleene Algebra with Observations: from Hypotheses to Completeness

Tobias Kappé·Paul Brunet·Alexandra Silva·Jana Wagemaker·Fabio Zanasi
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Abstract

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 $\mathsf{while}$-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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Tobias Kappé, Paul Brunet, Alexandra Silva, Jana Wagemaker, Fabio Zanasi. 2020-02-22. Concurrent Kleene Algebra with Observations: from Hypotheses to Completeness. https://doi.org/10.1007/978-3-030-45231-5_20

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