A Bi-Categorical Axiomatisation of Concurrent Graph Rewriting

A Bi-Categorical Axiomatisation of Concurrent Graph Rewriting (1999)

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by Fabio Gadducci , Reiko Heckel , Mercé Llabrés

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Datum	Value	Source
TITLE	A Bi-Categorical Axiomatisation of Concurrent Graph Rewriting	user correction - Legacy Corrections
AUTHOR NAME	Fabio Gadducci	user correction
AUTHOR AFFIL	Un. of Edinburgh, Division of Informatics, Laboratory for Foundations of Computer Science	user correction
AUTHOR NAME	Reiko Heckel	user correction
AUTHOR AFFIL	Un. of Paderborn, Department of Mathematics and Computer Science	user correction
AUTHOR NAME	Mercé Llabrés	user correction
AUTHOR AFFIL	Un. of the Balearic Islands, Department of Mathematics and Computer Science	user correction
ABSTRACT	In this paper the concurrent semantics of double-pushout (DPO) graph rewriting, which is classically defined in terms of shift-equivalence classes of graph derivations, is axiomatised via the construction of a free monoidal bi-category. In contrast to a previous attempt based on 2-categories, the use of bi-categories allows to define rewriting on concrete graphs. Thus, the problem of composition of isomorphism classes of rewriting sequences is avoided. Moreover, as a first step towards the recovery of the full expressive power of the formalism via a purely algebraic description, the concept of disconnected rules is introduced, i.e., rules whose interface graphs are made of disconnected nodes and edges only. It is proved that, under reasonable assumptions, rewriting via disconnected rules enjoys similar concurrency properties like in the classical approach.	user correction
YEAR	1999	user correction - Legacy Corrections
CITATIONS	31 found	ParsCit 1.0