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Order algebras: a quantitative model of interaction

Published online by Cambridge University Press:  13 February 2017

EMMANUEL BEFFARA
EMMANUEL BEFFARA*
Affiliation:
Institut de Mathématiques de Luminy, Aix Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453, Marseille, France Email: emmanuel.beffara@univ-amu.fr
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Abstract

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A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This algebraic structure is shown to provide faithful interpretations of finitary process algebras, for an extension of the standard notion of testing semantics, leading to a model that is both denotational (in the sense that the internal workings of processes are ignored) and non-interleaving. Constructions on algebras and their subspaces enjoy a good structure that make them (nearly) a model of differential linear logic, showing that the underlying approach to the representation of non-determinism as linear combinations is the same.

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