Specifying graph languages with type graphs

Corradini, Andrea; König, Barbara; Nolte, Dennis

doi:10.1016/j.jlamp.2019.01.005

Cited by 10 publications

(13 citation statements)

References 20 publications

(34 reference statements)

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“…, we would get that x ∈ img(β E ), due to property (9), which is a contradiction. We can hence conclude that f ′ E (x) ∈ E A , which implies that f E (x) must be of the form (e, s, t, l) ∈ E ⟨ϕ⟩ .…”

Section: Construction Of the Materialization In The Category Of Graphsmentioning

confidence: 90%

“…The main theme of the paper is "simultaneous" rewriting of entire sets of objects of a category by means of rewriting a single abstract object that represents a collection of structures-the language of the abstract object. The simplest example of an abstract structure is a plain object of a category to which we associate the language of objects that can be mapped to it; the formal definition is as follows (see also [10]).…”

Section: Languagesmentioning

confidence: 99%

“…In particular we will use ordered monoids in order to annotate objects. Similar annotations have already been studied in [21] in the context of type systems and in [10] with the aim of studying decidability and closure properties, but not for abstract rewriting. A tuple (M, +, −, ≤), where (M, +, ≤) is an ordered monoid and − is a binary operation on M, is called an ordered monoid with subtraction.…”

Section: Annotated Objectsmentioning

confidence: 99%

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Rewriting Abstract Structures: Materialization Explained Categorically

Corradini

Heindel

König

et al. 2019

Lecture Notes in Computer Science

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The paper develops an abstract (over-approximating) semantics for double-pushout rewriting of graphs and graph-like objects. The focus is on the socalled materialization of left-hand sides from abstract graphs, a central concept in previous work. The first contribution is an accessible, general explanation of how materializations arise from universal properties and categorical constructions, in particular partial map classifiers, in a topos. Second, we introduce an extension by enriching objects with annotations and give a precise characterization of strongest post-conditions, which are effectively computable under certain assumptions.Abstract interpretation [12] is a fundamental static analysis technique that applies not only to conventional programs but also to general infinite-state systems. Shape analysis [32], a specific instance of abstract interpretation, pioneered an approach for analyzing pointer structures that keeps track of information about the "heap topology", e.g., out-degrees or existence of certain paths. One central idea of shape analysis is materialization, which arises as companion operation to summarizing distinct objects that share relevant properties. Materialization, a.k.a. partial concretization, is also fundamental in verification approaches based on separation logic [6,5,25], where it is also known as rearrangement [28], a special case of frame inference. Shape analysis-construed in a wide sense-has been adapted to graph transformation [31], a general purpose modelling language for systems with dynamically evolving topology, such as network protocols and cyber-physical systems. Motivated by earlier work of shape analysis for graph transformation [33,4,1,2,30,29], we want to put the materialization operation on a new footing, widening the scope of shape analysis.A natural abstraction mechanism for transition systems with graphs as states "summarizes" all graphs over a specific shape graph. Thus a single graph is used as abstraction ⋆ Partially supported by AFOSR.⊳ A rewriting formalism for graph abstractions that lifts the rule-based rewriting from single graphs to abstract graphs; it is developed for (abstract) objects in a topos.⊳ We characterize the materialization operation for abstract objects in a topos in terms of partial map classifiers, giving a sound and complete description of all occurrences of right-hand sides of rules obtained by rewriting an abstract object.→ Sec. 3 ⊳ We decorate abstract objects with annotations from an ordered monoid and extend abstract rewriting to abstract objects with annotations. For the specific case of graphs, we consider global annotations (counting the nodes and edges in a graph), local annotations (constraining the degree of a node), and path annotations (constraining the existence of paths between certain nodes). → Sec. 4 ⊳ We show that abstract rewriting with annotations is sound and, with additional assumptions, complete. Finally, we even derive strongest post-conditions for the case of graph rewriting with annotations. → Sec. 5Related work: ...

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Section: Construction Of the Materialization In The Category Of Graphsmentioning

confidence: 90%

Section: Languagesmentioning

confidence: 99%

Section: Annotated Objectsmentioning

confidence: 99%

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Rewriting Abstract Structures: Materialization Explained Categorically

Corradini

Heindel

König

et al. 2019

Lecture Notes in Computer Science

Self Cite

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show abstract

“…For space considerations, we omit the precise handling of attributes from this paper as none of the four key properties depend on attributes. For metamodels, we use the notations of the Eclipse Modeling Framework (EMF) [90], but our concepts could easily be adapted to other frameworks of typed and attributed graphs such as [21,28].…”

Section: Metamodels and Instance Modelsmentioning

confidence: 99%

Towards the Automated Generation of Consistent, Diverse, Scalable and Realistic Graph Models

Varró

Semeráth

Szárnyas

et al. 2018

Graph Transformation, Specifications, and Nets

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Automated model generation can be highly beneficial for various application scenarios including software tool certification, validation of cyber-physical systems or benchmarking graph databases to avoid tedious manual synthesis of models. In the paper, we present a long-term research challenge how to generate graph models specific to a domain which are consistent, diverse, scalable and realistic at the same time. We provide foundations for a class of model generators along a refinement relation which operates over partial models with 3-valued representation and ensures that subsequently derived partial models preserve the truth evaluation of well-formedness constraints in the domain. We formally prove completeness, i.e. any finite instance model of a domain can be generated by model generator transformations in finite steps and soundness, i.e. any instance model retrieved as a solution satisfies all well-formedness constraints. An experimental evaluation is carried out in the context of a statechart modeling tool to evaluate the trade-off between different characteristics of model generators.

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“…DrAGoM (short for: Directed Abstract Graphs over Multiplicities) [49] is a prototype tool to handle and manipulate multiply annotated type graphs originally defined in [19,20]. The main application of DrAGoM is to check invariants of GTS in the framework of abstract graph rewriting.…”

Section: Strongest Postconditionmentioning

confidence: 99%

Analysis of Graph Transformation Systems: Native vs Translation-based Techniques

Heckel¹,

Lambers²,

Saadat³

2019

Electron. Proc. Theor. Comput. Sci.

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The paper summarises the contributions in a session at GCM 2019 presenting and discussing the use of native and translation-based solutions to common analysis problems for Graph Transformation Systems (GTSs). In addition to a comparison of native and translation-based techniques in this area, we explore design choices for the latter, s.a. choice of logic and encoding method, which have a considerable impact on the overall quality and complexity of the analysis. We substantiate our arguments by citing literature on application of theorem provers, model checkers, and SAT/SMT solver in GTSs, and conclude with a general discussion from a software engineering perspective, including comments from the workshop participants, and recommendations on how to investigate important design choices in the future.

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Specifying graph languages with type graphs

Cited by 10 publications

References 20 publications

Rewriting Abstract Structures: Materialization Explained Categorically

Rewriting Abstract Structures: Materialization Explained Categorically

Towards the Automated Generation of Consistent, Diverse, Scalable and Realistic Graph Models

Analysis of Graph Transformation Systems: Native vs Translation-based Techniques

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