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arXiv · 1410.4235

Convolution, Separation and Concurrency

Brijesh Dongol·Ian J. Hayes·Georg Struth
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Abstract

A notion of convolution is presented in the context of formal power series together with lifting constructions characterising algebras of such series, which usually are quantales. A number of examples underpin the universality of these constructions, the most prominent ones being separation logics, where convolution is separating conjunction in an assertion quantale; interval logics, where convolution is the chop operation; and stream interval functions, where convolution is used for analysing the trajectories of dynamical or real-time systems. A Hoare logic is constructed in a generic fashion on the power series quantale, which applies to each of these examples. In many cases, commutative notions of convolution have natural interpretations as concurrency operations.

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Brijesh Dongol, Ian J. Hayes, Georg Struth. 2014-10-15. Convolution, Separation and Concurrency. https://arxiv.org/abs/1410.4235

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