A UTP Semantics of pGCL as a Homogeneous Relation

Bresciani, Riccardo; Butterfield, Andrew

doi:10.1007/978-3-642-30729-4_14

Cited by 9 publications

(21 citation statements)

References 21 publications

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“…Incorporation of probabilities into formal program semantics has also been investigated within the Unifying Theories of Programming (UTP) framework [HS06,BB12,SZ13]. In [BB12], the authors present an encoding of the semantics of the probabilistic guarded command language (pGCL) in UTP.…”

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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Section: Related Workmentioning

confidence: 99%

Integrating stochastic reasoning into Event-B development

2015

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“…We have previously presented an encoding of the semantics of the probabilistic guarded command language (pGCL) in the UTP framework [BB11,BB12]. This encoding captures pGCL programs as predicate-transformers, on predicates over probability before-and after-distributions.…”

Section: Utpmentioning

confidence: 99%

A Probabilistic Theory of Designs Based on Distributions

Bresciani

Butterfield

2013

Unifying Theories of Programming

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Abstract. We present a theory of designs based on functions from the state space to real numbers, which we term distributions. This theory uses predicates, in the style of UTP, based on homogeneous relations between distributions, and is richer than the standard UTP theory of designs as it allows us to reason about probabilistic programs; the healthiness conditions H1-H4 of the standard theory are implicitly accounted for in the distributional theory we present. In addition we propose a Galois connection linkage between our distribution-based model of probabilistic designs, and the standard UTP model of (non-probabilistic) designs.

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“…We have previously used this to encode the semantics of pGCL in the UTP framework [BB11,BB12b]; moreover we have proposed a probabilistic theory of designs [BB12a], which we will briefly present in §3.2 after having presented the standard one.…”

Section: Utpmentioning

confidence: 99%

“…After having given a probabilistic UTP semantics to pGCL [BB11,BB12b] and having presented a probabilistic theory of designs [BB12a], we have started to look into the possibility of using our framework to have a probabilistic version of CSP : as the UTP theory of CSP is built on that of designs, we aim at building a theory of pCSP starting from that of probabilistic designs. The task turned out to be not so straightforward, posing interesting challenges which we find worthy of discussion in the present paper.…”

Section: Introductionmentioning

confidence: 99%

From Distributions to Probabilistic Reactive Programs

Bresciani

Butterfield

2013

Theoretical Aspects of Computing – ICTAC 2013

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Abstract. We have introduced probability in the UTP framework by using functions from the state space to real numbers, which we term distributions, that are embedded in the predicates describing the different program constructs. This has allowed us to derive a probabilistic theory of designs starting from a probabilistic version of the relational theory, and continuing further down this road we can get to a theory of probabilistic reactive programs. This paper presents the route that connects these steps, and discusses the challenges lying ahead in view of a probabilistic CSP based on distributions.

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A UTP Semantics of pGCL as a Homogeneous Relation

Cited by 9 publications

References 21 publications

Integrating stochastic reasoning into Event-B development

Integrating stochastic reasoning into Event-B development

A Probabilistic Theory of Designs Based on Distributions

From Distributions to Probabilistic Reactive Programs

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