Relabelling in Graph Transformation

Habel, Annegret; Plump, Detlef

doi:10.1007/3-540-45832-8_12

Cited by 55 publications

(105 citation statements)

References 11 publications

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“…We begin by briefly reviewing labelled graphs and the double-pushout approach to graph transformation with relabelling (see [7] for details).…”

Section: Attributed Graph Transformation Via Rule Schematamentioning

confidence: 99%

“…We denote such a derivation by G ⇒ r,g H. The requirement that the pushouts in Figure 1 are natural ensures that the pushout complement D in Figure 1 is uniquely determined by rule r, graph G and morphism g [7,Theorem 1]. Figure 2(b) demonstrates that non-natural pushout complements need not be unique.…”

Section: Double-pushout Approach With Relabellingmentioning

confidence: 99%

“…We therefore use the double-pushout approach with partially labelled interface graphs as a formal basis [7]. This approach is also the foundation of the graph programming language GP 2 [15].…”

Section: Introductionmentioning

confidence: 99%

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Attributed Graph Transformation via Rule Schemata: Church-Rosser Theorem

Hristakiev

Plump

2016

Software Technologies: Applications and Foundations

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Abstract. We present an approach to attributed graph transformation which requires neither infinite graphs containing data algebras nor auxiliary edges that link graph items with their attributes. Instead, we use the double-pushout approach with relabelling and extend it with rule schemata which are instantiated to ordinary rules prior to application. This framework provides the formal basis for the graph programming language GP 2. In this paper, we abstract from the data algebra of GP 2, define parallel independence of rule schema applications, and prove the Church-Rosser Theorem for our approach. The proof relies on the Church-Rosser Theorem for partially labelled graphs and adapts the classical proof by Ehrig and Kreowski, bypassing the technicalities of adhesive categories.

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“…We begin by briefly reviewing labelled graphs and the double-pushout approach to graph transformation with relabelling (see [7] for details).…”

Section: Attributed Graph Transformation Via Rule Schematamentioning

confidence: 99%

Section: Double-pushout Approach With Relabellingmentioning

confidence: 99%

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Attributed Graph Transformation via Rule Schemata: Church-Rosser Theorem

Hristakiev

Plump

2016

Software Technologies: Applications and Foundations

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“…We review basic notions of the double-pushout approach to graph transformation, using a version that allows unlabelled nodes [12]. Rules with unlabelled nodes allow to relabel nodes and, in addition, represent sets of totally labelled rules because unlabelled nodes in the left-hand side act as placeholders for arbitrarily labelled nodes.…”

Section: Graphs Rules and Derivationsmentioning

confidence: 99%

“…In [12] it is shown that for rule r and injective morphism g given, there exists such a direct derivation if and only if g satisfies the dangling condition: no node in g(L) − g(K) must be incident to an edge in G − g(L). If this condition is satisfied, then r and g determine D and H uniquely up to isomorphim and H can be constructed (up to isomorphism) from G as follows: (1) Remove all nodes and edges in g(L) − g(K), obtaining a subgraph D ′ .…”

Section: Graphs Rules and Derivationsmentioning

confidence: 99%

Graph Transformation in Constant Time

Dodds

Plump

2006

Lecture Notes in Computer Science

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Abstract. We present conditions under which graph transformation rules can be applied in time independent of the size of the input graph: graphs must contain a unique root label, nodes in the left-hand sides of rules must be reachable from the root, and nodes must have a bounded outdegree. We establish a constant upper bound for the time needed to construct all graphs resulting from an application of a fixed rule to an input graph. We also give an improved upper bound under the stronger condition that all edges outgoing from a node must have distinct labels. Then this result is applied to identify a class of graph reduction systems that define graph languages with a linear membership test. In a case study we prove that the (non-context-free) language of balanced binary trees with backpointers belongs to this class.

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Reducibility between Classes of Port Graph Grammar

Stewart

2002

Journal of Computer and System Sciences

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This paper introduces a general notion of static-port graph grammar (PGG) that encompasses existing formalisms that have been independently proposed, such as linear graph grammars, interaction nets and partial sharing graphs. These formalisms provide a computational framework for asynchronous computation that respects a very rigorous notion of local interaction, and have proven a suitable basis for the internal representation of program and data in the compilation of high-level programming languages for distributed execution. The general class of PGGs introduced in this paper provides a more expressive computational framework, still possessing asynchronous concurrency but which has a reduction mechanism that is complex and non-local. The increased expressiveness of this calculus is shown by means of a motivating example of concurrent pattern matching. However, the nonlocality of the calculus renders it unsuitable for direct implementation. The paper introduces a class of simple PGGs, a local rewriting calculus suitable for distributed implementation. The central result of the paper is to show how the general class of PGGs may be reduced to the simple PGGs, in a manner that fully preserves all the potential for concurrent rewriting present in the original. # 2002 Elsevier Science (USA)

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Relabelling in Graph Transformation

Cited by 55 publications

References 11 publications

Attributed Graph Transformation via Rule Schemata: Church-Rosser Theorem

Attributed Graph Transformation via Rule Schemata: Church-Rosser Theorem

Graph Transformation in Constant Time

Reducibility between Classes of Port Graph Grammar

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