Graph-grammars: An algebraic approach

Ehrig, Hartmut; Pfender, Michael; Schneider, Hans

doi:10.1109/swat.1973.11

Cited by 382 publications

(245 citation statements)

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“…This is one of the most commonly used algebraic approaches to rewriting, alternative to the double pushout (dpo) approach [10], where some subtle complications due to the inhibiting effects of dpo rewriting are avoided.…”

Section: Introductionmentioning

confidence: 99%

Unfolding Grammars in Adhesive Categories

Baldan

Corradini

Heindel

et al. 2009

Algebra and Coalgebra in Computer Science

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Abstract. We generalize the unfolding semantics, previously developed for concrete formalisms such as Petri nets and graph grammars, to the abstract setting of (single pushout) rewriting over adhesive categories. The unfolding construction is characterized as a coreflection, i.e. the unfolding functor arises as the right adjoint to the embedding of the category of occurrence grammars into the category of grammars. As the unfolding represents potentially infinite computations, we need to work in adhesive categories with "well-behaved" colimits of ω-chains of monomorphisms. Compared to previous work on the unfolding of Petri nets and graph grammars, our results apply to a wider class of systems, which is due to the use of a refined notion of grammar morphism.

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Section: Introductionmentioning

confidence: 99%

Unfolding Grammars in Adhesive Categories

Baldan

Corradini

Heindel

et al. 2009

Algebra and Coalgebra in Computer Science

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“…Transformations follow the double-pushout approach, with monomorphisms as matches [13]. We use a model of sociallydriven evolution of opinions [11] to illustrate our concepts.…”

Section: Assumptionmentioning

confidence: 99%

Transformation and Refinement of Rigid Structures

Danos

Heckel

Sobociński

2014

Graph Transformation

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Abstract. Stochastic rule-based models of networks and biological systems are hard to construct and analyse. Refinements help to produce systems at the right level of abstraction, enable analysis techniques and mappings to other formalisms. Rigidity is a property of graphs introduced in Kappa to support stochastic refinement, allowing to preserve the number of matches for rules in the refined system. In this paper: 1) we propose a notion of rigidity in an axiomatic setting based on adhesive categories; 2) we show how the rewriting of rigid structures can be defined systematically by requiring matches to be open maps reflecting structural features which ensure that rigidity is preserved; and 3) we obtain in our setting a notion of refinement which generalises that in Kappa, and allows a rule to be partitioned into a set of rules which are collectively equivalent to the original. We illustrate our approach with an example of a social network with dynamic topology.

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“…The algebraic approach to graph grammars has been presented for the first time in [5] in order to generalize Chomsky grammars from strings to graphs. That approach is currently known as double-pushout approach, because derivations are based on two pushout constructions in the category of graphs and total graph morphisms.…”

Section: Introductionmentioning

confidence: 99%