Resolution-Like Theorem Proving for High-Level Conditions

Pennemann, Karl-Heinz

doi:10.1007/978-3-540-87405-8_20

Cited by 32 publications

(35 citation statements)

References 16 publications

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“…Secondly, there are analysis techniques that explore the state space directly such as model-based testing [69,70,71] or model checking [72,73]. Moreover, based on the formal foundation of graph transformation, it is possible to apply theorem proving to graph transformation [74,75]. In [76], for example, we already verified behavior preservation of a model transformation (see [76]) specified with TGGs using theorem proving.…”

Section: Discussionmentioning

confidence: 99%

Graph Transformations for MDE, Adaptation, and Models at Runtime

Giese

Lambers

Becker

et al. 2012

Formal Methods for Model-Driven Engineering

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Abstract. Software evolution and the resulting need to continuously adapt the software is one of the main challenges for software engineering. The model-driven development movement therefore aims at improving the longevity of software by keeping the development artifacts more consistent and better changeable by employing models and to a certain degree automated model operations. Another trend are systems that tackle the challenge at runtime by being able to adapt their structure and behavior to be more flexible and operate in more dynamic environments (e.g., context-aware software, autonomic computing, self-adaptive software). Finally, models at runtime, where the benefits of model-driven development are employed at runtime to support adaptation capabilities, today lead towards a unification of both ideas. In this paper, we present graph transformations and show that they can be employed to engineer solutions for all three outlined cases. Furthermore, we will even be able to demonstrate that graph transformation based technology has the potential to also unify all three cases in a single scenario where models at runtime and runtime adaptation is linked with classical MDE. Therefore, we at first provide an introduction in graph transformations, then present the related techniques of Story Pattern and Triple Graph Grammars, and demonstrate how with the help of both techniques model transformations, adaptation behavior and runtime model framework work. In addition, we show that due to the formal underpinning analysis becomes possible and report about a number of successful examples.

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Section: Discussionmentioning

confidence: 99%

Graph Transformations for MDE, Adaptation, and Models at Runtime

Giese

Lambers

Becker

et al. 2012

Formal Methods for Model-Driven Engineering

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show abstract

“…There exist a number of example native approaches as well as translation-based approaches to both problems. For example, Pennemann [50] presents a native theorem prover, whereas Schneider et al [63] and Semerth et al [65] present native SAT solvers for graph conditions. Example translation-based approaches [39,28,66] map the SAT solving problem to target domains such as relational logic [35] and constraint logic programming.…”

Section: Sat-solving and Automated Reasoningmentioning

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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“…Therefore, our results hold for replacement-capable structures such as Petri-nets, graphs, and hypergraphs. [HPR06] conditions graphs theorem prover [Pen08b] sat. solver [Pen08a] yes/no/ unknown converter [HP09] 1st-order logic +graph axioms Vampire Darwin Paradox …”

Section: Preconditionmentioning

confidence: 99%

“…We have successfully presented our work on renowned international conferences in the research area of graph transformation [HPR06,HP06,Pen08a,Pen08b] and published our results in established journals in theoretical computer science [EEHP06,HP09]. Our work revived the interest in graph-based conditions, and was picked up, for instance, in [OEP08,Ore08].…”

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confidence: 91%

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Development of Correct Graph Transformation Systems

Pennemann

Lecture Notes in Computer Science

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Graph transformation has many application areas in computer science, such as software engineering or the design of concurrent and distributed systems. Being a visual modeling technique, graph transformation has the potential to play a decisive role in the development of increasingly larger and complex systems. However, the use of visual modeling techniques alone does not guarantee the correctness of a design. In context of rising standards for trustworthy systems, there is a growing need for the verification of graph transformation systems and programs. The research of appropriate methods for this purpose is the topic of this thesis.The primary goal is to obtain the capability to decide graphical program specifications. These specifications consists of a graphical precondition, a graph program, and a graphical postcondition. As usual, such a specification is said to be correct, if all those system states satisfy the postcondition that are reachable by applying the program on a start state satisfying the precondition. In the considered programs, the selection, deletion, addition and deselection of a graph's nodes and edges are the elementary constructs that can be composed to more complex programs by non-deterministic choice, sequential composition and iteration. The resulting programming language is computationally complete and is able to model transactions that deal with an unbounded number of nodes and edges. As language for the specification of state properties, graph conditions are investigated and used. We show that graph conditions provide an intuitive formalism for first-order structural properties and are suited to infer knowledge about the behavior of graph transformation systems and programs.According to Dijkstra, the correctness of program specifications can be shown by constructing a weakest precondition of the program relative to the postcondition and checking whether the specified precondition implies the weakest precondition. Hence the correctness problem of program specifications is reduced to an implication problem of conditions. In this thesis, it is shown how to construct weakest preconditions for graph programs and graph conditions. Following a dual approach, a sound and complete satisfiability iv Development of Correct Graph Transformation Systems algorithm for graph conditions is investigated and a fragment of conditions is identified, for which the algorithm decides. On the other hand, a resolutionbased calculus for graph conditions is presented and its soundness is proven. Implementations of the aforementioned deciders for conditions are compared with existing theorem provers and satisfiability solvers for first-order logic by verifying three case studies: a railroad control, an access control for computer systems, and, as an external example, a car platoon maneuver protocol.The research is done within the framework of the so-called weak adhesive high-level replacement categories. Therefore, the results will be applicable to different kinds of graph replacement systems and Petri n...

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Resolution-Like Theorem Proving for High-Level Conditions

Cited by 32 publications

References 16 publications

Graph Transformations for MDE, Adaptation, and Models at Runtime

Graph Transformations for MDE, Adaptation, and Models at Runtime

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

Development of Correct Graph Transformation Systems

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