Refinement algebra for probabilistic programs

Meinicke, Larissa; Solin, Kim

doi:10.1007/s00165-009-0111-1

Cited by 9 publications

(5 citation statements)

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“…They cover various semantic models in a uniform algebraic fashion. Further applications have concerned residuals (e.g., to define generalised modal operators as in [65,57]), predicate transformer semantics (e.g., as demonic refinement algebra [66,59] or command/design algebra [47,18,19]), probabilistic programs [42,64,43], game algebra [51,52], hybrid systems [26,27], neighbourhood logic [25] and linked object structures and separation logic [13,7]. There is even a greater variety of applications outside the realm of program semantics.…”

Section: Discussionmentioning

confidence: 99%

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Building Structured Theories

Möller

2011

Relational and Algebraic Methods in Computer Science

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Section: Discussionmentioning

confidence: 99%

“…The symmetrical axioms that describe "iteration at the right" may need adjustments due to the application circumstances (e.g. in probabilistic algebras) [42,64,43]. Infinite iteration is added using seminal ideas from [53]; the axiomatisation follows [5].…”

Section: Iterationmentioning

confidence: 99%

Building Structured Theories

Möller

2011

Relational and Algebraic Methods in Computer Science

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“…A connection between probabilistic reasoning and program refinement has been investigated by Meinicke and Solin [MS10]. The authors introduce a refinement algebra for reasoning about probabilistic program transformations.…”

Section: Related Workmentioning

confidence: 99%

Integrating stochastic reasoning into Event-B development

2015

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Dependability is a property of a computer system to deliver services that can be justifiably trusted. Formal modelling and verification techniques are widely used for development of dependable computer-based systems to gain confidence in the correctness of system design. Such techniques include Event-B-a state-based formalism that enables development of systems correct-by-construction. While Event-B offers a scalable approach to ensuring functional correctness of a system, it leaves aside modelling of non-functional critical properties, e.g., reliability and responsiveness, that are essential for ensuring dependability of critical systems. Both reliability, i.e., the probability of the system to function correctly over a given period of time, and responsiveness, i.e., the probability of the system to complete execution of a requested service within a given time bound, are defined as quantitative stochastic measures. In this paper, we propose an extension of the Event-B semantics to enable stochastic reasoning about dependability-related non-functional properties of cyclic systems. We define the requirements that a cyclic system should satisfy and introduce the notions of reliability and responsiveness refinement. Such an extension integrates reasoning about functional correctness and stochastic modelling of non-functional characteristics into the formal system development. It allows the designer to ensure that a developed system does not only correctly implement its functional requirements but also satisfies given non-functional quantitative constraints.

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“…The refinement oriented theory of programs uses demonic choice, usually written ⊓, as a primitive (see e.g. [30,31]). A demonic choice can be regarded as a probabilistic choice with unknown probabilities.…”

Section: Related Workmentioning

confidence: 99%

Instruction sequence notations with probabilistic instructions

Bergstra,

Middelburg

2009

Preprint

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This paper concerns instruction sequences that contain probabilistic instructions, i.e. instructions that are themselves probabilistic by nature. We propose several kinds of probabilistic instructions, provide an informal operational meaning for each of them, and discuss related work. On purpose, we refrain from providing an ad hoc formal meaning for the proposed kinds of instructions. We also discuss the approach of projection semantics, which was introduced in earlier work on instruction sequences, in the light of probabilistic instruction sequences.

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Refinement algebra for probabilistic programs

Cited by 9 publications

References 30 publications

Building Structured Theories

Building Structured Theories

Integrating stochastic reasoning into Event-B development

Instruction sequence notations with probabilistic instructions

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