Algebraic Approaches to Graph Transformation – Part Ii: Single Pushout Approach and Comparison With Double Pushout Approach

Ehrig, Hartmut; Heckel, Reiko; Korff, Martin; Lowe, M. J. S.; Ribeiro, Leila; Wagner, Annika; Corradini, Andrea

doi:10.1142/9789812384720_0004

Cited by 200 publications

(141 citation statements)

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“…We will first define a family of categories of graphs and graph morphisms, being as general as possible by defining graph structures [5], which include different forms of graphs such as directed graphs and hypergraphs. The simplest graph structure signature has two sorts: node and edge and two operator symbols s, t ∈ OP edge,node standing for "source" and "target".…”

Section: The Dpo Approach To Graph Rewritingmentioning

confidence: 99%

Deriving Bisimulation Congruences in the DPO Approach to Graph Rewriting

Ehrig

König

2004

Lecture Notes in Computer Science

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Abstract. Motivated by recent work on the derivation of labelled transitions and bisimulation congruences from unlabelled reaction rules, we show how to solve this problem in the DPO (double-pushout) approach to graph rewriting. Unlike in previous approaches, we consider graphs as objects, instead of arrows, of the category under consideration. This allows us to present a very simple way of deriving labelled transitions (called rewriting steps with borrowed context) which smoothly integrates with the DPO approach, has a very constructive nature and requires only a minimum of category theory. The core part of this paper is the proof sketch that the bisimilarity based on rewriting with borrowed contexts is a congruence relation.

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Section: The Dpo Approach To Graph Rewritingmentioning

confidence: 99%

Deriving Bisimulation Congruences in the DPO Approach to Graph Rewriting

Ehrig

König

2004

Lecture Notes in Computer Science

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“…SPO is capable of removing nodes and their incident edges from the graph, including dangling edges [20]. Algebraic approaches can be extended by additional application conditions, such as existence and non-existence of certain nodes and edges [21], as well as conditions that are repeated frequently in the original graph and known as nested conditions [22].…”

Section: Prov Graph Transformation System (Prov-gts)mentioning

confidence: 99%

Obscuring Provenance Confidential Information via Graph Transformation

Hussein

Moreau

Sassone

2015

Trust Management IX

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Abstract. Provenance is a record that describes the people, institutions, entities, and activities involved in producing, influencing, or delivering a piece of data or a thing. In particular, the provenance of information is crucial in deciding whether information is to be trusted. PROV is a recent W3C specification for sharing provenance over the Web. However, provenance records may expose confidential information, such as identity of agents or specific attributes of entities or activities. It is therefore essential for confidential information to be obscured before sharing provenance. This paper describes PROV-GTS, a provenance graph transformation system, whose principled definition is based on PROV properties, and which seeks to avoid false independencies and false dependencies. PROV-GTS is shown to preserve graph integrity, to be terminating and to be confluent.

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“…If G =⇒ r H, one says that G directly derives H by applying r. There are many possibilities to choose rules and their applications. Types of rules may vary from the more restrictive ones, like edge replacement [4] or node replacement [8], to the more general ones, like double-pushout rules [2], single-pushout rules [6], or PROGRES rules [17].…”

Section: Rule Basesmentioning

confidence: 99%

Typing of Graph Transformation Units

Klempien-Hinrichs

Kreowski

Kuske

2004

Lecture Notes in Computer Science

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Abstract. The concept of graph transformation units in its original sense is a structuring principle for graph transformation systems which allows the interleaving of rule applications with calls of imported units in a controlled way. The semantics of a graph transformation unit is a binary relation on an underlying type of graphs. In order to get a flexible typing mechanism for transformation units and a high degree of parallelism this paper introduces typed graph transformation units that transform k-tuples of typed input graphs into l-tuples of typed output graphs in a controlled and structured way. The transformation of the typed graph tuples is performed with actions that apply graph transformation rules and imported typed units simultaneously to the graphs of a tuple. The transformation process is controlled with control conditions and with graph tuple class expressions. The new concept of typed graph transformation units is illustrated with examples from the area of string parsing with finite automata.

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Algebraic Approaches to Graph Transformation – Part Ii: Single Pushout Approach and Comparison With Double Pushout Approach

Cited by 200 publications

References 0 publications

Deriving Bisimulation Congruences in the DPO Approach to Graph Rewriting

Deriving Bisimulation Congruences in the DPO Approach to Graph Rewriting

Obscuring Provenance Confidential Information via Graph Transformation

Typing of Graph Transformation Units

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