The boolean algebra of cubical areas as a tensor product in the category of semilattices with zero

Abstract : In this paper we describe a model of concurrency enjoying an algebraic structure reflecting the parallel composition. For the sake of simplicity we restrict to linear concurrent programs i.e. the ones with neither loops nor branchings. Such programs are given a semantics using cubical areas that we call geometric. The collection of all cubical areas admits a structure of tensor product in the category of semi-lattice with zero. These results naturally extend to fully fledged concurrent programs up to some technical tricks.
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Submitted on : Thursday, July 12, 2018 - 1:24:39 PM
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N. Ninin, E. Haucourt. The boolean algebra of cubical areas as a tensor product in the category of semilattices with zero. Proceedings 7th Interaction and Concurrency Experience, 2014, Jun 2014, Berlin, Germany. pp.60-66, ⟨10.4204/EPTCS.166.7⟩. ⟨cea-01836515⟩

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