Using PVS for Modeling and Verification of Probabilistic Connectors

Nawaz, M. Saqib; Sun, Min

doi:10.1007/978-3-030-31517-7_5

Cited by 5 publications

(9 citation statements)

References 22 publications

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“…All the experiments are performed on an HP laptop with a fifth generation Core i5 processor and 8 GB RAM. For the case study, we select our previous works [32], [33], where PVS is used for the analysis and verification of Reo connectors composed of untimed, timed and probabilistic channels. The main reason to select the proofs in [32], [33] is that we are extending the formalization framework to cover the stochastic [5] and hybrid [8] behavior of Reo connectors.…”

Section: Experiments and Resultsmentioning

confidence: 99%

“…For the case study, we select our previous works [32], [33], where PVS is used for the analysis and verification of Reo connectors composed of untimed, timed and probabilistic channels. The main reason to select the proofs in [32], [33] is that we are extending the formalization framework to cover the stochastic [5] and hybrid [8] behavior of Reo connectors. We believe that this proof learning approach will not only enable us to comprehend the proof process for stochastic and hybrid connectors but also can be considered far more effective in providing the necessary guidance to attain the proofs of such connectors.…”

Section: Experiments and Resultsmentioning

confidence: 99%

“…These predicates are similar to the untimed predicates with one of the time sequences is added by a t time delay. The probabilistic connectors behavior in [33] is formalized with timed data distribution (TDD), where T is a sequence of time points, and DD is a sequence of data distributions. For untimed/timed channels, data is defined as a positive type.…”

Section: A Case Studymentioning

confidence: 99%

“…Flow through and replicate operators can be achieved explicitly in PVS, whereas merge operator is defined inductively. The complete details on the specification for Reo channels, operators and predicates can be found in [32], [33], [38].…”

Section: A Case Studymentioning

confidence: 99%

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Proof Learning in PVS With Utility Pattern Mining

Nawaz

Fournier-Viger

2020

IEEE Access

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Interactive theorem provers (ITPs) are software tools that allow human users to write and verify formal proofs. In recent years, an emerging research area in ITPs is proof mining, which consists of identifying interesting proof patterns that can be used to guide the interactive proof process in ITPs. In previous studies, some data mining techniques, such as frequent pattern mining, have been used to analyze proofs to find frequent proof steps. Though useful, such models ignore the facts that not all proof steps are equally important. To address this issue, this paper proposes a novel proof mining approach based on finding not only frequent patterns but also high utility patterns to find proof steps of high importance (utility). A proof process learning approach is proposed based on high utility itemset mining (HUIM) for the PVS (Prototype Verification System) proof assistant. Proofs in PVS theories are first abstracted to a computerprocessable corpus, where each line represents a proof sequence and proof commands in proof sequences are associated with utilities representing their weightage (importance). HUIM techniques are then applied on the corpus to discover frequent proof steps/high utility patterns and their relationships with each other. Experimental results suggest that combining frequent pattern mining techniques, such as sequential pattern mining and high utility itemset mining, with proof assistants, such as PVS, is useful to learn and guide the proof development process. INDEX TERMS Frequent patterns, High utility itemset mining, Proof steps, Proof sequences, PVS.

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Section: Experiments and Resultsmentioning

confidence: 99%

Section: Experiments and Resultsmentioning

confidence: 99%

Section: A Case Studymentioning

confidence: 99%

Section: A Case Studymentioning

confidence: 99%

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Proof Learning in PVS With Utility Pattern Mining

Nawaz

Fournier-Viger

2020

IEEE Access

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“…Rigorous formalization of connectors has been proved crucial for the efficient modeling and analysis of coordinated software systems [BMM11,SZ18]. Connectors have been studied extensively in systems modeling with alternative frameworks and expressiveness, including process algebras [BCD00,BMM11] and category theory [BLM06,BMM11], while they have been also supported by several architectural description languages (ADLs for short) [Ozk18,NS19,SZ18].…”

Section: Introductionmentioning

confidence: 99%

A formal algebraic approach for the quantitative modeling of connectors in architectures

Chrysovalanti¹,

Pittou²

2022

Preprint

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In this paper we propose an algebraic formalization of connectors in the quantitative setting in order to address the performance issues related with the architectures of component-based systems. For this, we firstly introduce a weighted Algebra of Interactions over a set of ports and a commutative and idempotent semiring. The algebra serves sufficiently for modeling wellknown coordination schemes in the weighted setup. In turn, we introduce and study a weighted Algebra of Connectors over a set of ports and a commutative and idempotent semiring, which extends the weighted Algebra of Interactions with types that express two different modes of synchronization, in particular, Rendezvous and Broadcast. We show the expressiveness of the algebra by modeling several weighted connectors. Moreover, we derive two subalgebras, namely the weighted Algebra of Synchrons and of Triggers, and study their properties. Finally, we introduce a weighted congruence relation for connectors and provide conditions for proving congruence between distinct weighted connectors.

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