Concurrent Kleene Algebra: Free Model and Completeness

@article{Kapp2018ConcurrentKA,
  title={Concurrent Kleene Algebra: Free Model and Completeness},
  author={Tobias Kapp{\'e} and Paul Brunet and Alexandra Silva and Fabio Zanasi},
  journal={ArXiv},
  year={2018},
  volume={abs/1710.02787}
}
Concurrent 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… 
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