Concurrent Kleene Algebra: Free Model and Completeness
2018; Springer Science+Business Media; Linguagem: Inglês
10.1007/978-3-319-89884-1_30
ISSN1611-3349
AutoresTobias Kappé, Paul Brunet, Alexandra Silva, Fabio Zanasi,
Tópico(s)Computability, Logic, AI Algorithms
ResumoConcurrent Kleene Algebra (CKA) was introduced by Hoare, Moeller, Struth and Wehrman in 2009 as a framework to reason about concurrent programs. We prove that the axioms for CKA with bounded parallelism are complete for the semantics proposed in the original paper; consequently, these semantics are the free model for this fragment. This result settles a conjecture of Hoare and collaborators. Moreover, the technique developed to this end allows us to establish a Kleene Theorem for CKA, extending an earlier Kleene Theorem for a fragment of CKA.
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