Hierarchical Graph Transformation Revisited

Padberg, Julia

doi:10.1007/978-3-319-61470-0_2

Cited by 4 publications

(2 citation statements)

References 19 publications

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“…Many other examples concern comma category constructions, with a number of illustrative examples provided in Table 1. More intricate examples still have been developed in the context of so-called hierarchical graphs, which are obtained via commacategorical constructions along various notions of super-power functors, and whose adhesivity properties have been studied in [56,57] (see also [44]). 2) undirected multigraphs [29] *…”

Section: Many Of the Examples Listed Inmentioning

confidence: 99%

Fundamentals of Compositional Rewriting Theory

Behr¹,

Harmer²,

Krivine³

2022

Preprint

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A foundational theory of compositional categorical rewriting theory is presented, based on a collection of fibrationlike properties that collectively induce and structure intrinsically the large collection of lemmata used in the proofs of theorems such as concurrency and associativity. The resulting highly generic proofs of these theorems are given; it is noteworthy that the proof of the concurrency theorem takes only a few lines and, while that of associativity remains somewhat longer, it would be unreadably long if written directly in terms of the basic lemmata. In addition to improving, or even enabling, the readability of human-written proofs, we anticipate that this more generic and modular style of writing proofs should organize and inform the production of formalized proofs in a proof assistant such as Coq or Isabelle. A curated list of known instances of our framework is used to conclude the paper with a detailed discussion of the conditions under which the Double Pushout and Sesqui-Pushout semantics of graph transformation are compositional.

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Section: Many Of the Examples Listed Inmentioning

confidence: 99%

Fundamentals of Compositional Rewriting Theory

Behr¹,

Harmer²,

Krivine³

2022

Preprint

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“…Distributed hierarchical graphs form the basis upon which the agent-based OWL semantic web ontological model is built and in which graph transformations can take place at various levels of abstraction [42]. Other interesting hierarchical representations include that of L-Graphs in which edges and nodes are labelled by graphs [41], M -adhesive Graph Transformation Systems [38] that provide a generic algebraic definition to cater for varying graphs types, that of the verbose property graphs used in graph analytics [28], and the implementation found in [45]; that also makes use of attributes and multi-typed sub-graphs. [38] also contains details of multi-hierarchical graphs and graph groupings.…”

Section: H-graphsmentioning

confidence: 99%

Attributed Hierarchical Port Graphs and Applications

Ene

Fernández

Pinaud

2018

Electron. Proc. Theor. Comput. Sci.

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We present attributed hierarchical port graphs (AHP) as an extension of port graphs that aims at facilitating the design of modular port graph models for complex systems. AHP consist of a number of interconnected layers, where each layer defines a port graph whose nodes may link to layers further down the hierarchy; attributes are used to store user-defined data as well as visualisation and run-time system parameters. We also generalise the notion of strategic port graph rewriting (a particular kind of graph transformation system, where port graph rewriting rules are controlled by user-defined strategies) to deal with AHP following the Single Push-out approach. We outline examples of application in two areas: functional programming and financial modelling.

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A new criterion for $$\mathcal {M}, \mathcal {N}$$-adhesivity, with an application to hierarchical graphs

Castelnovo

Gadducci

Miculan

2022

Lecture Notes in Computer Science

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Adhesive categories provide an abstract framework for the algebraic approach to rewriting theory, where many general results can be recast and uniformly proved. However, checking that a model satisfies the adhesivity properties is sometimes far from immediate. In this paper we present a new criterion giving a sufficient condition for $$\mathcal {M},\mathcal {N}$$ M , N -adhesivity, a generalisation of the original notion of adhesivity. We apply it to several existing categories, and in particular to hierarchical graphs, a formalism that is notoriously difficult to fit in the mould of algebraic approaches to rewriting and for which various alternative definitions float around.

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Hierarchical Graph Transformation Revisited

Cited by 4 publications

References 19 publications

Fundamentals of Compositional Rewriting Theory

Fundamentals of Compositional Rewriting Theory

Attributed Hierarchical Port Graphs and Applications

A new criterion for $$\mathcal {M}, \mathcal {N}$$-adhesivity, with an application to hierarchical graphs

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