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Rule algebras for adhesive categories

Rule algebras for adhesive categories
Rule algebras for adhesive categories
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.
Behr, Nicolas
051a6dee-acc5-427d-84ff-699ea2674747
Sobocinski, Pawel
439334ab-2826-447b-9fe5-3928be3fd4fd
Behr, Nicolas
051a6dee-acc5-427d-84ff-699ea2674747
Sobocinski, Pawel
439334ab-2826-447b-9fe5-3928be3fd4fd

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

Record type: Conference or Workshop Item (Paper)

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.

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More information

Published date: 4 September 2018
Venue - Dates: Computer Science Logic 2018<br/>, Birmingham, United Kingdom, 2018-09-04 - 2018-09-07

Identifiers

Local EPrints ID: 422642
URI: http://eprints.soton.ac.uk/id/eprint/422642
PURE UUID: 9852a3c1-9c16-4243-9b0b-f6449dcfdf5a

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Date deposited: 27 Jul 2018 16:30
Last modified: 27 Jul 2018 16:30

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