Simulation as a Proof Method for Data Refinement

Roever, Willem-Paul de; Engelhardt, Kai

doi:10.1017/cbo9780511663079.003

Cited by 7 publications

(14 citation statements)

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“…Both continuous and discrete models "run" for the same amount of time, T Stop , and the output relation (37) gives an estimate for the discrepancy between the continuous and discrete states reached in the two models after that time. The states themselves consist of two components, the displacements and the velocities.…”

Section: Corroborationmentioning

confidence: 99%

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Formalising the Continuous/Discrete Modeling Step

Banach

Zhu

et al. 2011

Electron. Proc. Theor. Comput. Sci.

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Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete domains. The difference between the two is quantified using generic results from ODE theory, and these estimates can be compared with the exact solutions. Such results do not fit well into a conventional model based refinement framework; however they can be accommodated into a model based retrenchment. The retrenchment is described, and the way it can interface to refinement development on both the continuous and discrete sides is outlined. The approach is compared to what can be achieved using hybrid systems techniques.

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Section: Corroborationmentioning

confidence: 99%

“…Conventional model based formal refinement technologies (see for example [37,19,38,1,34,43,2]) are based on purely discrete mathematical and logical concepts. These turn out to be ill suited to modeling and formally developing applications whose usual models are best expressed using continuous mathematics.…”

Section: Introductionmentioning

confidence: 99%

Formalising the Continuous/Discrete Modeling Step

Banach

Zhu

et al. 2011

Electron. Proc. Theor. Comput. Sci.

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“…Influenced by the established notions of refinement of the formal methods community [4,11], we sought a relationship that would permit us to verify whether results of the later safety assessment preserve key commitments of the earlier, typically less detailed, iterations. We were further concerned with comparing results of the assessments performed at different levels of granularity and using different modelling methods and tools.…”

Section: 'Lightweight Refinement' Relationmentioning

confidence: 99%

Application of the 'lightweight refinement relation to establishing confidence in safety assessment models

Lisagor¹,

Kelly²

2010

5th IET International Conference on System Safety 2010

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This paper presents a 'lightweight refinement' relation that enables rational comparison of safety assessment models of a system. The comparison process contributes to establishing confidence in adequacy of the models by identification of apparent inconsistencies that require explicit justification.The paper further demonstrates how the 'machinery' of refinement can be applied to individual models to identify key 'simulation cases' and aid the task of model review.

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“…To replace this by a local criterion, abstraction relations are introduced that relate inputs and outputs of operations at the abstract and the concrete level. de Roever and Engelhardt's book contains further information [10]. Program refinement often requires inequational reasoning.…”

Section: Simulation Laws For Data Refinementmentioning

confidence: 99%

“…L-andL-simulations are also complete for data refinement, but proofs in the literature are pointwise (cf. [10]) and additional effort would be required to extract a purely relation-algebraic proof. We leave this for future work.…”

Section: ⊓ ⊔mentioning

confidence: 99%

On Automating the Calculus of Relations

Höfner

Struth

Automated Reasoning

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Abstract. Relation algebras provide abstract equational axioms for the calculus of binary relations. They name an established area of mathematics with various applications in computer science. We prove more than hundred theorems of relation algebras with off-the-shelf automated theorem provers. This yields a basic calculus from which more advance applications can be explored. Here, we present two examples from the formal methods literature. Our experiments not only further underline the feasibility of automated deduction in complex algebraic structures and provide theorem proving benchmarks, they also pave the way for lifting established formal methods such as B or Z to a new level of automation.

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Simulation as a Proof Method for Data Refinement

Cited by 7 publications

References 0 publications

Formalising the Continuous/Discrete Modeling Step

Formalising the Continuous/Discrete Modeling Step

Application of the 'lightweight refinement relation to establishing confidence in safety assessment models

On Automating the Calculus of Relations

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