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Rule Algebras for Adhesive Categories

Authors Nicolas Behr, Pawel Sobocinski

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Author Details

Nicolas Behr
  • IRIF, Université Paris-Diderot (Paris 07), France
Pawel Sobocinski
  • ECS, University of Southampton, UK

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Nicolas Behr and Pawel Sobocinski. Rule Algebras for Adhesive Categories. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 11:1-11:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Concurrency
  • Mathematics of computing → Markov processes
  • Adhesive categories
  • rule algebras
  • Double Pushout (DPO) rewriting


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