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

Nicolas Ninin; Emmanuel Haucourt

doi:10.4204/EPTCS.166.7

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

Nicolas Ninin
, Emmanuel Haucourt

CEA/UVSQ/CNRS

Research output: Contribution to journal › Conference article › peer-review

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.

Original language	English
Pages (from-to)	60-66
Number of pages	7
Journal	Electronic Proceedings in Theoretical Computer Science, EPTCS
Volume	166
DOIs	https://doi.org/10.4204/EPTCS.166.7
Publication status	Published - 26 Oct 2014
Externally published	Yes
Event	7th Interaction and Concurrency Experience, ICE 2014 - Berlin, Germany Duration: 6 Jun 2014 → …

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

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