Order algebras: a quantitative model of interaction

Emmanuel Beffara (1)

1 I2M - Institut de Mathématiques de Marseille

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.

Domaines: Logique en informatique [cs.LO]; Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Emmanuel Beffara. Order algebras: a quantitative model of interaction. Mathematical Structures in Computer Science, 2018, ⟨10.1017/S0960129516000360⟩. ⟨hal-00429610v3⟩