Concurrent Kleene Algebra with Tests and Branching Automata

Authors

Peter Jipsen, Chapman UniversityFollow
M. Andrew Moshier, Chapman UniversityFollow

Document Type

Article

Publication Date

12-30-2015

Abstract

We introduce concurrent Kleene algebra with tests (CKAT) as a combination of Kleene algebra with tests (KAT) of Kozen and Smith with concurrent Kleene algebras (CKA), introduced by Hoare, Möller, Struth and Wehrman. CKAT provides a relatively simple algebraic model for reasoning about semantics of concurrent programs. We generalize guarded strings to guarded series-parallel strings , or gsp-strings, to give a concrete language model for CKAT. Combining nondeterministic guarded automata of Kozen with branching automata of Lodaya and Weil one obtains a model for processing gsp-strings in parallel. To ensure that the model satisfies the weak exchange law (x‖y)(z‖w)≤(xz)‖(yw) of CKA, we make use of the subsumption order of Gischer on the gsp-strings. We also define deterministic branching automata and investigate their relation to (nondeterministic) branching automata.

To express basic concurrent algorithms, we define concurrent deterministic flowchart schemas and relate them to branching automata and to concurrent Kleene algebras with tests.

Comments

NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Logical and Algebraic Methods in Programming. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Logical and Algebraic Methods in Programming in 2015. DOI: 10.1016/j.jlamp.2015.12.005

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Recommended Citation

P. Jipsen, M. Andrew Moshier, Concurrent Kleene algebra with tests and branching automata, J. Log. Algebraic Methods Program. (2015), http://dx.doi.org/10.1016/j.jlamp.2015.12.005

Peer Reviewed

1

Copyright

Elsevier

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.