The Boolean Algebra of Cubical Areas as a Tensor Product in the Category of Semilattices with Zero

In this paper we describe a model of concurrency together with an algebraic structure reflecting the parallel composition. For the sake of simplicity we restrict to linear concurrent programs i.e. the ones with no loops nor branching. Such programs are given a semantics using cubical areas. Such a...

Full description

Bibliographic Details
Main Authors:	Nicolas Ninin, Emmanuel Haucourt
Format:	Article
Language:	English
Published:	Open Publishing Association 2014-10-01
Series:	Electronic Proceedings in Theoretical Computer Science
Online Access:	http://arxiv.org/pdf/1410.7470v1

id	doaj-0dda472fd0c54004b1cfc4457c46b948
record_format	Article
spelling	doaj-0dda472fd0c54004b1cfc4457c46b9482020-11-24T23:42:43ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802014-10-01166Proc. ICE 2014606610.4204/EPTCS.166.7:2The Boolean Algebra of Cubical Areas as a Tensor Product in the Category of Semilattices with ZeroNicolas Ninin0Emmanuel Haucourt1 CEA, LIST and University Paris-Sud, France CEA, LIST In this paper we describe a model of concurrency together with an algebraic structure reflecting the parallel composition. For the sake of simplicity we restrict to linear concurrent programs i.e. the ones with no loops nor branching. Such programs are given a semantics using cubical areas. Such a semantics is said to be geometric. The collection of all these cubical areas enjoys 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.http://arxiv.org/pdf/1410.7470v1
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Nicolas Ninin Emmanuel Haucourt
spellingShingle	Nicolas Ninin Emmanuel Haucourt The Boolean Algebra of Cubical Areas as a Tensor Product in the Category of Semilattices with Zero Electronic Proceedings in Theoretical Computer Science
author_facet	Nicolas Ninin Emmanuel Haucourt
author_sort	Nicolas Ninin
title	The Boolean Algebra of Cubical Areas as a Tensor Product in the Category of Semilattices with Zero
title_short	The Boolean Algebra of Cubical Areas as a Tensor Product in the Category of Semilattices with Zero
title_full	The Boolean Algebra of Cubical Areas as a Tensor Product in the Category of Semilattices with Zero
title_fullStr	The Boolean Algebra of Cubical Areas as a Tensor Product in the Category of Semilattices with Zero
title_full_unstemmed	The Boolean Algebra of Cubical Areas as a Tensor Product in the Category of Semilattices with Zero
title_sort	boolean algebra of cubical areas as a tensor product in the category of semilattices with zero
publisher	Open Publishing Association
series	Electronic Proceedings in Theoretical Computer Science
issn	2075-2180
publishDate	2014-10-01
description	In this paper we describe a model of concurrency together with an algebraic structure reflecting the parallel composition. For the sake of simplicity we restrict to linear concurrent programs i.e. the ones with no loops nor branching. Such programs are given a semantics using cubical areas. Such a semantics is said to be geometric. The collection of all these cubical areas enjoys 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.
url	http://arxiv.org/pdf/1410.7470v1
work_keys_str_mv	AT nicolasninin thebooleanalgebraofcubicalareasasatensorproductinthecategoryofsemilatticeswithzero AT emmanuelhaucourt thebooleanalgebraofcubicalareasasatensorproductinthecategoryofsemilatticeswithzero AT nicolasninin booleanalgebraofcubicalareasasatensorproductinthecategoryofsemilatticeswithzero AT emmanuelhaucourt booleanalgebraofcubicalareasasatensorproductinthecategoryofsemilatticeswithzero
_version_	1725503346515640320

The Boolean Algebra of Cubical Areas as a Tensor Product in the Category of Semilattices with Zero

Similar Items