Nested Quantification in Graph Transformation Rules

Rensink, Arend

doi:10.1007/11841883_1

Cited by 21 publications

(16 citation statements)

References 15 publications

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“…Defining more general ACs, whose graphs are not restricted to be connected, is also under consideration. Following the ideas in [31] it could also be interesting to permit quantification on rules themselves (and not only the ACs). We also plan to deepen in the analysis of critical pairs, especially analysing the new kind of conflicts arising due to our ACs, as well as by using the negative initial digraphs for the analysis.…”

Section: Discussionmentioning

confidence: 99%

Matrix Graph Grammars with Application Conditions

Velasco

Lara

2010

Fundamenta Informaticae

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In the Matrix approach to graph transformation we represent simple digraphs and rules with Boolean matrices and vectors, and the rewriting is expressed using Boolean operators only. In previous works, we developed analysis techniques enabling the study of the applicability of rule sequences, their independence, state reachability and the minimal graph able to fire a sequence.In the present paper we improve our framework in two ways. First, we make explicit (in the form of a Boolean matrix) some negative implicit information in rules. This matrix (called nihilation matrix) contains the elements that, if present, forbid the application of the rule (i.e. potential dangling edges, or newly added edges, which cannot be already present in the simple digraph). Second, we introduce a novel notion of application condition, which combines graph diagrams together with monadic second order logic. This allows for more flexibility and expressivity than previous approaches, as well as more concise conditions in certain cases. We demonstrate that these application conditions can be embedded into rules (i.e. in the left hand side and the nihilation matrix), and show that the applicability of a rule with arbitrary application conditions is equivalent to the applicability of a sequence of plain rules without application conditions. Therefore, the analysis of the former is equivalent to the analysis of the latter, showing that in our framework no additional results are needed for the study of application conditions. Moreover, all analysis techniques of [21,22] for the study of sequences can be applied to application conditions.Typing. A type is assigned to each node in G ÔM, V Õ by a function from the set of nodes V to a set of types T , type : V T . In Fig. 1 types are represented as an extra column in the matrices, the numbers before the colon distinguish elements of the same type. For edges we use the types of their source and target nodes. Definition 2.3. (Typed Simple Digraph)A typed simple digraph G T ÔG M , typeÕ over a set of types T , is made of a simple digraph G M ÔM, V Õ, and a function from the set of nodes V to the set of types T , type : V T .Next, we define the notion of partial morphism between typed simple digraphs. Definition 2.4. (Typed Simple Digraph Morphism)where DomÔf Õ is the domain of the partial function f . Productions.A production, or rule, p : L R is a morphism of typed simple digraphs. Using a static formulation, a rule is represented by two typed simple digraphs that encode the left and right hand sides (LHS and RHS). The matrices and vectors of these graphs are arranged so that the elements identified by morphism p match (this is called completion, see below). Definition 2.5. (Static Formulation of Production)A production p : L R is statically represented as p ÔL ÔL E , L V , type L Õ; R ÔR E , R V , type R ÕÕ, where E stands for edges and V for vertices.A production adds and deletes nodes and edges, therefore using a dynamic formulation, we can encode the rule's pre-condition (its LHS) together with...

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Section: Discussionmentioning

confidence: 99%

Matrix Graph Grammars with Application Conditions

Velasco

Lara

2010

Fundamenta Informaticae

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“…To delete these nodes, we have to check conditions that repeat frequently in the host graph and have a universal nature which can only be represented using nested graph predicates [25]. In our system, we adopt the approach defined in [25,26] limited to graph predicates of depth three and one rule application. Each nested rule consists of two parts: the nested graph predicate for rule matching, represented by a root (LHS) and a set of universal-existential pairs (u i , e i ), and an RHS for rule application.…”

Section: Nested Graph Predicatementioning

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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“…Researchers at Twente introduced two ways by which richer families of graphs could be matched and rewritten using something akin to pattern graphs. The first method, initiated by Rensink, uses quantified graph transformation rules, where subgraphs are attached to a tree of alternating quantifiers [18,19]. Unlike the transformation rules we consider, this method allows matchings to be non-full on all vertices in a pattern graph, so an edge in the pattern can be interpreted as an existentially-quantified statement on the attached subgraph, rather than a requirement that all incident edges must be matched.…”

Section: Related Workmentioning

confidence: 99%

Pattern graph rewrite systems

Kissinger

Merry

Soloviev

2014

Electron. Proc. Theor. Comput. Sci.

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String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric representations of string diagrams, amenable to automated reasoning about diagrammatic theories via graph rewrite systems. In this extended abstract, we show how the power of such rewrite systems can be greatly extended by introducing pattern graphs, which provide a means of expressing infinite families of rewrite rules where certain marked subgraphs, called !-boxes ("bang boxes"), on both sides of a rule can be copied any number of times or removed. After reviewing the string graph formalism, we show how string graphs can be extended to pattern graphs and how pattern graphs and pattern rewrite rules can be instantiated to concrete string graphs and rewrite rules. We then provide examples demonstrating the expressive power of pattern graphs and how they can be applied to study interacting algebraic structures that are central to categorical quantum mechanics.Comment: In Proceedings DCM 2012, arXiv:1403.757

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Nested Quantification in Graph Transformation Rules

Cited by 21 publications

References 15 publications

Matrix Graph Grammars with Application Conditions

Matrix Graph Grammars with Application Conditions

Obscuring Provenance Confidential Information via Graph Transformation

Pattern graph rewrite systems

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