Verifying Probabilistic Programs Using a Hoare like Logic

Hartog, J.I. den

doi:10.1007/3-540-46674-6_11

Cited by 14 publications

(23 citation statements)

References 7 publications

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“…Logics supporting such reasoning have branched in two main directions. Firstly, Hoare-style [27,21,6] and dynamic logics [9,17] have been developed building upon denotational semantics of probabilistic programs [16]. The second approach enriches temporal modalities with probabilistic bounds [10,13,23].…”

Section: Introductionmentioning

confidence: 99%

“…A sound Hoare logic with a truth-functional state logic was presented in [6] and completeness for a fragment of the Hoare-logic is shown for iteration-free programs. In order to deal with alternative composition, a probabilistic sum construct (ξ 1 + ξ 2 ) is introduced in [6].…”

Section: Introductionmentioning

confidence: 99%

“…In order to deal with alternative composition, a probabilistic sum construct (ξ 1 + ξ 2 ) is introduced in [6]. Intuitively, the formula (ξ 1 + ξ 2 ) is satisfied by a (sub)-probability measure µ if µ can be be written as the sum of two measures µ 1 and µ 2 which satisfy ξ 1 and ξ 2 respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Intuitively, the formula (ξ 1 + ξ 2 ) is satisfied by a (sub)-probability measure µ if µ can be be written as the sum of two measures µ 1 and µ 2 which satisfy ξ 1 and ξ 2 respectively. The drawback of [6] is that no axiomatization is given for the state assertion logic. The essential obstacle in achieving a complete axiomatization for the state language in [6] is the probabilistic sum construct.…”

Section: Introductionmentioning

confidence: 99%

“…The drawback of [6] is that no axiomatization is given for the state assertion logic. The essential obstacle in achieving a complete axiomatization for the state language in [6] is the probabilistic sum construct.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Reasoning About States of Probabilistic Sequential Programs

Chadha¹,

Mateus²,

Sernadas³

2006

Computer Science Logic

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Abstract. A complete and decidable propositional logic for reasoning about states of probabilistic sequential programs is presented. The state logic is then used to obtain a sound Hoare-style calculus for basic probabilistic sequential programs. The Hoare calculus presented herein is the first probabilistic Hoare calculus with a complete and decidable state logic that has truth-functional propositional (not arithmetical) connectives. The models of the state logic are obtained exogenously by attaching sub-probability measures to valuations over memory cells. In order to achieve complete and recursive axiomatization of the state logic, the probabilities are taken in arbitrary real closed fields.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Reasoning About States of Probabilistic Sequential Programs

Chadha¹,

Mateus²,

Sernadas³

2006

Computer Science Logic

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Quantum software testing: State of the art

Barrera

Guzmán

Polo

et al. 2021

J Software Evolu Process

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Quantum computing is expected to exponentially outperform classic computing on a broad set of problems, including encryption, machine learning, and simulations. It has an impact yet to explore on all software lifecycle's processes and techniques. Testing quantum software raises a significant number of challenges due to the unique properties of quantum physics-such as superposition and entanglementand the stochastic behavior of quantum systems. It is, therefore, an open research issue. In this work, we offer a systematic mapping study of quantum software testing engineering, presenting a comprehensive view of the current state of the art. The main identified trends in testing techniques are (1) the statistic approaches based on repeated measurements and (2) the use of Hoare-like logics to reason about software correctness.Another relevant line of research is reversible circuit testing, which is partially applicable to quantum software unitary testing. Finally, we have observed a flourishing of secondary studies and frameworks supporting testing processes from 2018 onwards. | INTRODUCTIONQuantum computing (QC) processes information using quantum mechanics principles. In comparison to classic computing (CC), this paradigm has the potential to solve specific problems with exponential speedup. 1 QC has a wide number of applications and is expected to outperform CC in two particular kinds of computations 2 :• Applications that involve large amounts of parallel computing such as encryption, 3 big data, 4 optimization, 5 or machine learning. 6• Simulation of quantum natural phenomena, such as chemistry, 7 physics, 8 and materials science. 9With the growing accessibility of quantum computers and simulators, many concerns have arisen related to quantum software and its lifecycle and quality. Quantum software will be developed in a large-scale industrial context in the same way that classic software is nowadays produced. This implies that quantum software must be developed, operated, and maintained in a systematic, disciplined, and quantifiable manner; that is, quantum software development must be supported by a yet nonexisting body of knowledge on quantum software engineering (QSE) that must be developed to avoid a quantum software crisis. Some authors have already voiced the need to "build a community for QSE that focuses on devising methods, tools, and processes for developing quantum software systems efficiently" 10 and the need for an agenda that sets out a solid, rigorous software engineering (SE) discipline for quantum systems. 11 Others are convinced that QC could bring a "new SE golden age", 12 identifying several priority areas to be developed in QSE.

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A Calculus of Chaos in Stochastic Compilation

Breuer¹,

Pickin

2020

Lecture Notes in Computer Science

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Verifying Probabilistic Programs Using a Hoare like Logic

Cited by 14 publications

References 7 publications

Reasoning About States of Probabilistic Sequential Programs

Reasoning About States of Probabilistic Sequential Programs

Quantum software testing: State of the art

A Calculus of Chaos in Stochastic Compilation

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