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Documents authored by Vignudelli, Valeria

Document
(Co)algebraic pearls
DOI: 10.4230/LIPIcs.CALCO.2021.11
Presenting Convex Sets of Probability Distributions by Convex Semilattices and Unique Bases ((Co)algebraic pearls)

Authors: Filippo Bonchi, Ana Sokolova, and Valeria Vignudelli

Published in: LIPIcs, Volume 211, 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)

Abstract
We prove that every finitely generated convex set of finitely supported probability distributions has a unique base. We apply this result to provide an alternative proof of a recent result: the algebraic theory of convex semilattices presents the monad of convex sets of probability distributions.
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Filippo Bonchi, Ana Sokolova, and Valeria Vignudelli. Presenting Convex Sets of Probability Distributions by Convex Semilattices and Unique Bases ((Co)algebraic pearls). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bonchi_et_al:LIPIcs.CALCO.2021.11,
  author =	{Bonchi, Filippo and Sokolova, Ana and Vignudelli, Valeria},
  title =	{{Presenting Convex Sets of Probability Distributions by Convex Semilattices and Unique Bases}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{11:1--11:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-212-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{211},
  editor =	{Gadducci, Fabio and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.11},
  URN =		{urn:nbn:de:0030-drops-153666},
  doi =		{10.4230/LIPIcs.CALCO.2021.11},
  annote =	{Keywords: Convex sets of distributions monad, Convex semilattices, Unique base}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2020.28
Monads and Quantitative Equational Theories for Nondeterminism and Probability

Authors: Matteo Mio and Valeria Vignudelli

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

Abstract
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 extended 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.
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Matteo Mio and Valeria Vignudelli. Monads and Quantitative Equational Theories for Nondeterminism and Probability. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{mio_et_al:LIPIcs.CONCUR.2020.28,
  author =	{Mio, Matteo and Vignudelli, Valeria},
  title =	{{Monads and Quantitative Equational Theories for Nondeterminism and Probability}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{28:1--28:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.28},
  URN =		{urn:nbn:de:0030-drops-128407},
  doi =		{10.4230/LIPIcs.CONCUR.2020.28},
  annote =	{Keywords: Computational Effects, Monads, Metric Spaces, Quantitative Algebras}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2018.4
Proof Techniques for Program Equivalence in Probabilistic Higher-Order Languages (Invited Talk)

Authors: Valeria Vignudelli

Published in: LIPIcs, Volume 108, 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)

Abstract
While the theory of functional higher-order languages, starting from lambda-calculi, is a well-established research field, it is only in recent years that the operational semantics of higher-order languages with probabilistic operators has started to be extensively studied. A fundamental notion in the semantics of programming languages is that of program equivalence. In higher-order languages, program equivalence is generally formalized as a contextual equivalence [Morris, 1968], which can be hard to prove directly. This has motivated the study of proof techniques for contextual equivalence, from inductive ones, such as logical relations [Andrew Pitts, 2005], to coinductive ones, mainly in the form of bisimulations [Abramsky, 1990]. In this talk I will discuss proof techniques for program equivalence in languages combining higher-order and probabilistic features. Several operational methods, traditionally developed in a deterministic setting, have been adapted to probabilistic higher-order languages [Ales Bizjak and Lars Birkedal, 2015; Dal Lago et al., 2014; Raphaëlle Crubillé and Ugo Dal Lago, 2014]. I will discuss these proof methods and focus on bisimulation-based techniques, showing how probabilities, combined with different language features, force a number of modifications to the definition of bisimulation [Crubillé et al., 2015; Sangiorgi and Vignudelli, 2016].
Cite as

Valeria Vignudelli. Proof Techniques for Program Equivalence in Probabilistic Higher-Order Languages (Invited Talk). In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 4:1-4:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{vignudelli:LIPIcs.FSCD.2018.4,
  author =	{Vignudelli, Valeria},
  title =	{{Proof Techniques for Program Equivalence in Probabilistic Higher-Order Languages}},
  booktitle =	{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)},
  pages =	{4:1--4:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{Kirchner, H\'{e}l\`{e}ne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2018.4},
  URN =		{urn:nbn:de:0030-drops-91749},
  doi =		{10.4230/LIPIcs.FSCD.2018.4},
  annote =	{Keywords: Lambda Calculus, Contextual Equivalence, Bisimulation, Probabilistic Programming Languages}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2016.35
Up-To Techniques for Generalized Bisimulation Metrics

Authors: Konstantinos Chatzikokolakis, Catuscia Palamidessi, and Valeria Vignudelli

Published in: LIPIcs, Volume 59, 27th International Conference on Concurrency Theory (CONCUR 2016)

Abstract
Bisimulation metrics allow us to compute distances between the behaviors of probabilistic systems. In this paper we present enhancements of the proof method based on bisimulation metrics, by extending the theory of up-to techniques to (pre)metrics on discrete probabilistic concurrent processes. Up-to techniques have proved to be a powerful proof method for showing that two systems are bisimilar, since they make it possible to build (and thereby check) smaller relations in bisimulation proofs. We define soundness conditions for up-to techniques on metrics, and study compatibility properties that allow us to safely compose up-to techniques with each other. As an example, we derive the soundness of the up-to-bisimilarity-metric-and-context technique. The study is carried out for a generalized version of the bisimulation metrics, in which the Kantorovich lifting is parametrized with respect to a distance function. The standard bisimulation metrics, as well as metrics aimed at capturing multiplicative properties such as differential privacy, are specific instances of this general definition.
Cite as

Konstantinos Chatzikokolakis, Catuscia Palamidessi, and Valeria Vignudelli. Up-To Techniques for Generalized Bisimulation Metrics. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 35:1-35:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{chatzikokolakis_et_al:LIPIcs.CONCUR.2016.35,
  author =	{Chatzikokolakis, Konstantinos and Palamidessi, Catuscia and Vignudelli, Valeria},
  title =	{{Up-To Techniques for Generalized Bisimulation Metrics}},
  booktitle =	{27th International Conference on Concurrency Theory (CONCUR 2016)},
  pages =	{35:1--35:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-017-0},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{59},
  editor =	{Desharnais, Jos\'{e}e and Jagadeesan, Radha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2016.35},
  URN =		{urn:nbn:de:0030-drops-61793},
  doi =		{10.4230/LIPIcs.CONCUR.2016.35},
  annote =	{Keywords: bisimulation, metrics, up-to techniques, Kantorovich, differential privacy}
}
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