Confluence of Graph Rewriting with Interfaces

Bonchi, Filippo; Gadducci, Fabio; Kissinger, Aleks; Sobociński, Paweł; Zanasi, Fabio

doi:10.1007/978-3-662-54434-1_6

Cited by 13 publications

(17 citation statements)

References 41 publications

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“…In [8], it is proven that confluence is decidable for terminating rewrite systems on graphs with an interface, which embed those considered in the present paper (as mentioned above, confluence is undecidable in general in graph rewriting). In our results, the rewrite rules we consider are not necessarily terminating (and equations are not even orientable in general).…”

Section: Related Worksupporting

confidence: 60%

A Superposition-Based Calculus for Diagrammatic Reasoning

Echahed

Echenim

Mhalla

et al. 2021

23rd International Symposium on Principles and Practice of Declarative Programming

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We introduce a class of rooted graphs which are expressive enough to encode various kinds of classical or quantum circuits. We then follow a set-theoretic approach to define rewrite systems over the considered graphs. Afterwards, we tackle the problem of equational reasoning with the graphs under study and we propose a new Superposition calculus to check the unsatisfiability of formulas consisting of equations or disequations over these graphs. We establish the soundness and refutational completeness of the calculus. CCS CONCEPTS• Theory of computation → Automated reasoning; Equational logic and rewriting.

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Section: Related Worksupporting

confidence: 60%

A Superposition-Based Calculus for Diagrammatic Reasoning

Echahed

Echenim

Mhalla

et al. 2021

23rd International Symposium on Principles and Practice of Declarative Programming

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“…Moreover, he also proved that (local) confluence of graph transformation systems is undecidable, even for terminating systems, as opposed to what happens in the area of term rewriting systems. However, recently, in [2] it is shown that confluence of terminating DPO transformation of graphs with interfaces is decidable. The authors explain that the reason is that interfaces play the same role as variables in term rewriting systems, where confluence is undecidable for terminating ground (i.e., without variables) systems, but decidable for non-ground ones.…”

Section: Related Workmentioning

confidence: 99%

Initial Conflicts for Transformation Rules with Nested Application Conditions

Lambers

Orejas

2020

Graph Transformation

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We extend the theory of initial conflicts in the framework of M-adhesive categories to transformation rules with ACs. We first show that for rules with ACs, conflicts are in general neither inherited from a bigger context any more, nor is it possible to find a finite and complete subset of finite conflicts as illustrated for the category of graphs. We define initial conflicts to be special so-called symbolic transformation pairs, and show that they are minimally complete (and in the case of graphs also finite) in this symbolic way. We show that initial conflicts represent a proper subset of critical pairs again. We moreover demonstrate that (analogous to the case of rules without ACs) for each conflict a unique initial conflict exists representing it. We conclude with presenting a sufficient condition illustrating important special cases for rules with ACs, where we do not only have initial conflicts being complete in a symbolic way, but also find complete (and in the case of graphs also finite) subsets of conflicts in the classical sense.

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“…One of the most popular graph rewriting approaches is known as double pushout (DPO) rewriting [9], and we shall now recall some of its basic notions in relation to linear hypergraphs. We use an extension of the traditional definition that introduces an 'interface' [4]. Intuitively, the pushout complement is G with L removed.…”

Section: Graph Rewritingmentioning

confidence: 99%

Rewriting Graphically with Symmetric Traced Monoidal Categories

Kaye¹

2020

Preprint

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We examine a variant of hypergraphs that we call linear hypergraphs, with the aim of creating a sound and complete graphical language for symmetric traced monoidal categories (STMCs). We first define the category of linear hypergraphs as a full subcategory of conventional (simple) hypergraphs, in which each vertex is either the source or the target of exactly one edge. The morphisms of a freely generated STMC can be then interpreted as linear hypergraphs, up to isomorphism (soundness). Moreover, any linear hypergraph is the representation of a unique STMC morphism, up to the equational theory of the category (completeness). This establishes linear hypergraphs as the graphical language of STMCs. Linear hypergraphs are then shown to form a partial adhesive category which means that a broad range of equational properties of some STMC can be specified as a graph rewriting system. The graphical language of digital circuits is presented as a case study.

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Confluence of Graph Rewriting with Interfaces

Cited by 13 publications

References 41 publications

A Superposition-Based Calculus for Diagrammatic Reasoning

A Superposition-Based Calculus for Diagrammatic Reasoning

Initial Conflicts for Transformation Rules with Nested Application Conditions

Rewriting Graphically with Symmetric Traced Monoidal Categories

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