Compositional bisimulation metric reasoning with Probabilistic Process Calculi

Gebler, Daniel; Larsen, Kim Guldstrand; Tini, Simone

doi:10.2168/lmcs-12(4:12)2016

Cited by 17 publications

(5 citation statements)

References 48 publications

(70 reference statements)

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“…We have introduced the Met monad Ĉ of non-empty convex sets of distributions equipped with the Hausdorff-Kantorovich distance, and we have proved that Ĉ is presented by the quantitative equational theory QTh CS of quantitative convex semilattices. This result provides the basis for a foundational understanding of equational reasoning about program distances in processes combining nondeterminism and probabilities, as in bisimulation and trace metrics [21, 25,46,5,17]. This opens several directions for future research.…”

Section: Discussionmentioning

confidence: 89%

Monads and Quantitative Equational Theories for Nondeterminism and Probability

Mio,

Vignudelli

2020

Preprint

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The monad of convex sets of probability distributions is a well-known tool for modelling the combination of nondeterministic and probabilistic computational effects. In this work we lift this monad from the category of sets to the category of metric spaces, by means of the Hausdorff and Kantorovich metric liftings. Our main result is the presentation of this lifted monad in terms of the quantitative equational theory of convex semilattices, using the framework of quantitative algebras recently introduced by Mardare, Panangaden and Plotkin. ACM Subject ClassificationTo be specified later.

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Section: Discussionmentioning

confidence: 89%

Monads and Quantitative Equational Theories for Nondeterminism and Probability

Mio,

Vignudelli

2020

Preprint

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“…The use of metrics for the analysis of systems stems from [GJS90, DGJP04, KN96] where, in a process algebraic setting, it is argued that metrics are indeed more informative than behavioural equivalences when quantitative information on the behaviour is taken into account. The Wasserstein lifting has then found several successful applications: from the definition of behavioural metrics (e.g., [vB05,CLT20b,GLT16,GT18]), to privacy [CGPX14, CCP18, CCP20] and machine learning (e.g., [ACB17, GAA + 17, TBGS18]). Usually, one can use behavioural metrics to quantify how well an implementation (I) meets its specification (S).…”

Section: Discussionmentioning

confidence: 99%

A framework to measure the robustness of programs in the unpredictable environment

Castiglioni¹,

Loreti²,

Tini³

2023

Logical Methods in Computer Science

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Due to the diffusion of IoT, modern software systems are often thought to control and coordinate smart devices in order to manage assets and resources, and to guarantee efficient behaviours. For this class of systems, which interact extensively with humans and with their environment, it is thus crucial to guarantee their correct behaviour in order to avoid unexpected and possibly dangerous situations. In this paper we will present a framework that allows us to measure the robustness of systems. This is the ability of a program to tolerate changes in the environmental conditions and preserving the original behaviour. In the proposed framework, the interaction of a program with its environment is represented as a sequence of random variables describing how both evolve in time. For this reason, the considered measures will be defined among probability distributions of observed data. The proposed framework will be then used to define the notions of adaptability and reliability. The former indicates the ability of a program to absorb perturbation on environmental conditions after a given amount of time. The latter expresses the ability of a program to maintain its intended behaviour (up-to some reasonable tolerance) despite the presence of perturbations in the environment. Moreover, an algorithm, based on statistical inference, is proposed to evaluate the proposed metric and the aforementioned properties. We use two case studies to the describe and evaluate the proposed approach.

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“…Finally, in the process-algebra setting, compositional reasoning about metrics has received some attention. Gebler et al [2016] used uniform continuity to reason about the distance between recursive processes in a compositional way, while Gebler and Tini [2018] recently defined specification formats that can check uniform continuity syntactically. syntactic manner.…”

Section: Asynchronous Rules For Bounding the Kantorovich Distancementioning

confidence: 99%

A pre-expectation calculus for probabilistic sensitivity

Aguirre

Barthe

Hsu

et al. 2021

Proc. ACM Program. Lang.

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Sensitivity properties describe how changes to the input of a program affect the output, typically by upper bounding the distance between the outputs of two runs by a monotone function of the distance between the corresponding inputs. When programs are probabilistic, the distance between outputs is a distance between distributions. The Kantorovich lifting provides a general way of defining a distance between distributions by lifting the distance of the underlying sample space; by choosing an appropriate distance on the base space, one can recover other usual probabilistic distances, such as the Total Variation distance. We develop a relational pre-expectation calculus to upper bound the Kantorovich distance between two executions of a probabilistic program. We illustrate our methods by proving algorithmic stability of a machine learning algorithm, convergence of a reinforcement learning algorithm, and fast mixing for card shuffling algorithms. We also consider some extensions: using our calculus to show convergence of Markov chains to the uniform distribution over states and an asynchronous extension to reason about pairs of program executions with different control flow.

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Compositional bisimulation metric reasoning with Probabilistic Process Calculi

Cited by 17 publications

References 48 publications

Monads and Quantitative Equational Theories for Nondeterminism and Probability

Monads and Quantitative Equational Theories for Nondeterminism and Probability

A framework to measure the robustness of programs in the unpredictable environment

A pre-expectation calculus for probabilistic sensitivity

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