Rule algebras for adhesive categories

Behr, Nicolas and Sobocinski, Pawel (2018) Rule algebras for adhesive categories. Computer Science Logic 2018<br/>, , Birmingham, United Kingdom. 04 - 07 Sep 2018.

Abstract

We show that every adhesive category gives rise to an associative algebra of rewriting rules induced by the notion of double-pushout (DPO) rewriting and the associated notion of concurrent production. In contrast to the original formulation of rule algebras in terms of relations between (a concrete notion of) graphs, here we work in an abstract categorical setting. Doing this, we extend the classical concurrency theorem of DPO rewriting and show that the composition of DPO rules along abstract dependency relations is, in a natural sense, an associative operation. If in addition the adhesive category possesses a strict initial object, the resulting rule algebra is also unital. We demonstrate that in this setting the canonical representation of the rule algebras is obtainable, which opens the possibility of applying the concept to define and compute the evolution of statistical moments of observables in stochastic DPO rewriting systems.

This record has no associated files available for download.

Contributors

Download statistics