Parallel rewriting of attributed graphs

Tour, Thierry Boy de la; Echahed, Rachid

doi:10.1016/j.tcs.2020.09.025

Cited by 4 publications

(10 citation statements)

References 8 publications

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“…It is of course possible to extend Definition 3 accordingly (see [1, 11.3] for the general definition of a limit). It would then be easy to prove that cellular automata can be represented by PCTs, with a single production rule (see also [4,Theorem 6.3]).…”

Section: Examplesmentioning

confidence: 99%

“…The present work stems from [4] where an algorithmic framework is proposed for rule-based deterministic parallel transformations of graphs whose vertices and arrows are mapped to sets of attributes. The rules are triples pL, K, Rq where K is a subgraph of L and the intersection of L and R (that stands for the object I in a weak span) is a subgraph of K. Parallel coherence is replaced with a more general effective deletion property that distinguishes graph items (vertices and arrows) from attributes.…”

Section: Conclusion and Related Workmentioning

confidence: 99%

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Parallel Coherent Graph Transformations

Tour

Echahed

2021

Recent Trends in Algebraic Development Techniques

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Cellular automata as well as simultaneous assignments in Python can be understood as the parallel application of local rules to a grid or an environment that can be easily represented as an attributed graph. Since the result of such transformations cannot generally be obtained by a sequential application of the involved rules, this situation infringes the standard notion of parallel independence. An algebraic approach with production rules of the form L Ð K Ð I Ñ R is adopted and a condition of parallel coherence more general than parallel independence is formulated, that enable the definition of the Parallel Coherent Transformation (PCT). This transformation supports a generalisation of the Parallelism Theorem in the theory of adhesive HLR categories, showing that the PCT yields the expected result of sequential rewriting steps when parallel independence holds. Categories of finitely attributed structures are proposed, in which PCTs are guaranteed to exist. These notions are introduced and illustrated on several detailed examples.

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Section: Examplesmentioning

confidence: 99%

Section: Conclusion and Related Workmentioning

confidence: 99%

Parallel Coherent Graph Transformations

Tour

Echahed

2021

Recent Trends in Algebraic Development Techniques

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“…It turns out that Definition 5.2 provides the expected characterization of sequential independence. The (rather long) proof of Theorem 5.3 can be found in [5].…”

Section: Parallel Independencementioning

confidence: 99%

“…M (x) = ∅ and therefore M has the effective deletion property. It has been shown in [5] that =⇒ R is deterministic up to isomorphism, that is, if G =⇒ R H, G ′ =⇒ R H ′ and G ≃ G ′ then H ≃ H ′ . In particular, it is possible to represent any cellular automaton by a suitable rule r and a class of graphs that correspond to configurations of the automaton (every vertex corresponds to a cell), such that =⇒ r (restricted to such graphs) is the transition function of the automaton.…”

Section: Parallel Rewritingmentioning

confidence: 99%

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Parallel Independence in Attributed Graph Rewriting

Tour¹

2021

Electron. Proc. Theor. Comput. Sci.

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In order to define graph transformations by the simultaneous application of concurrent rules, we have adopted in previous work a structure of attributed graphs stable by unions. We analyze the consequences on parallel independence, a property that characterizes the possibility to resort to sequential rewriting. This property turns out to depend not only on the left-hand side of rules, as in algebraic approaches to graph rewriting, but also on their right-hand side. It is then shown that, of three possible definitions of parallel rewriting, only one is convenient in the light of parallel independence.

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A Rule-Based Procedure for Graph Query Solving

Duval

Echahed

Prost

2023

Lecture Notes in Computer Science

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We consider a core language for graph queries. These queries, which may transform graphs to graphs, are seen as formulas to be solved with respect to graph databases. For this purpose, we first define a graph query algebra where some operations over graphs and sets of graph homomorphisms are specified. Then, the notion of pattern is introduced to represent a kind of recursively defined formula over graphs. The syntax and formal semantics of patterns are provided. Afterwards, we propose a new sound and complete procedure to solve patterns. This procedure, which is based on a set of rewriting rules, is terminating and develops only one needed derivation per pattern to be solved. Our procedure is generic in the sense that it can be adapted to different kinds of graph queries provided that the notions of graph and graph homomorphism are well defined.

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Parallel rewriting of attributed graphs

Cited by 4 publications

References 8 publications

Parallel Coherent Graph Transformations

Parallel Coherent Graph Transformations

Parallel Independence in Attributed Graph Rewriting

A Rule-Based Procedure for Graph Query Solving

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