Convolution as a Unifying Concept

Brijesh Dongol, Ian J. Hayes, Georg Struth
<span title="2016-02-17">2016</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="" style="color: black;">ACM Transactions on Computational Logic</a> </i> &nbsp;
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 proposed for
more &raquo; ... ng the trajectories of dynamical or real-time systems. A Hoare logic can be 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.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1145/2874773</a> <a target="_blank" rel="external noopener" href="">fatcat:czhzxgz5xne6xdfjsz2d6q3ka4</a> </span>
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