17 Search Results for "Mardare, Radu"

Document
Invited Talk
DOI: 10.4230/LIPIcs.CONCUR.2025.3
On-The-Fly Verification: Advancements in Dependency Graphs (Invited Talk)

Authors: Jiří Srba

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
Dependency graphs have emerged as a versatile and powerful formalism with wide-ranging applications in formal verification. In this extended abstract, we provide an overview of selected advancements in on-the-fly verification techniques based on dependency graphs, focusing on the recent developments, optimizations and generalizations of this generic verification framework.
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Jiří Srba. On-The-Fly Verification: Advancements in Dependency Graphs (Invited Talk). In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 3:1-3:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{srba:LIPIcs.CONCUR.2025.3,
  author =	{Srba, Ji\v{r}{\'\i}},
  title =	{{On-The-Fly Verification: Advancements in Dependency Graphs}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{3:1--3:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.3},
  URN =		{urn:nbn:de:0030-drops-239534},
  doi =		{10.4230/LIPIcs.CONCUR.2025.3},
  annote =	{Keywords: dependency graphs, Boolean equation systems, on-the-fly algorithms, fixed-point computation, applications}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.31
Compositional Reasoning for Parametric Probabilistic Automata

Authors: Hannah Mertens, Tim Quatmann, and Joost-Pieter Katoen

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
We establish an assume-guarantee (AG) framework for compositional reasoning about multi-objective queries in parametric probabilistic automata (pPA) - an extension to probabilistic automata (PA), where transition probabilities are functions over a finite set of parameters. We lift an existing framework for PA to the pPA setting, incorporating asymmetric, circular, and interleaving proof rules. Our approach enables the verification of a broad spectrum of multi-objective queries for pPA, encompassing probabilistic properties and (parametric) expected total rewards. Additionally, we introduce a rule for reasoning about monotonicity in composed pPAs.
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Hannah Mertens, Tim Quatmann, and Joost-Pieter Katoen. Compositional Reasoning for Parametric Probabilistic Automata. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 31:1-31:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mertens_et_al:LIPIcs.CONCUR.2025.31,
  author =	{Mertens, Hannah and Quatmann, Tim and Katoen, Joost-Pieter},
  title =	{{Compositional Reasoning for Parametric Probabilistic Automata}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{31:1--31:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.31},
  URN =		{urn:nbn:de:0030-drops-239810},
  doi =		{10.4230/LIPIcs.CONCUR.2025.31},
  annote =	{Keywords: Verification, Probabilistic systems, Assume-guarantee reasoning, Parametric Probabilistic Automata, Parameter synthesis}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.36
Explainability is a Game for Probabilistic Bisimilarity Distances

Authors: Emily Vlasman, Anto Nanah Ji, James Worrell, and Franck van Breugel

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
We revisit a game from the literature that characterizes the probabilistic bisimilarity distances of a labelled Markov chain. We illustrate how an optimal policy of the game can explain these distances. Like the games that characterize bisimilarity and probabilistic bisimilarity, the game is played on pairs of states and matches transitions of those states. To obtain more convincing and interpretable explanations than those provided by generic optimal policies, we restrict to optimal policies that delay reaching observably inequivalent state pairs for as long as possible (called 1-maximal) while quickly reaching equivalent ones (called 0-minimal). We present iterative algorithms that compute 1-maximal and 0-minimal policies and prove an exponential lower bound for the number of iterations of the algorithm that computes 1-maximal policies.
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Emily Vlasman, Anto Nanah Ji, James Worrell, and Franck van Breugel. Explainability is a Game for Probabilistic Bisimilarity Distances. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 36:1-36:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vlasman_et_al:LIPIcs.CONCUR.2025.36,
  author =	{Vlasman, Emily and Nanah Ji, Anto and Worrell, James and van Breugel, Franck},
  title =	{{Explainability is a Game for Probabilistic Bisimilarity Distances}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{36:1--36:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.36},
  URN =		{urn:nbn:de:0030-drops-239861},
  doi =		{10.4230/LIPIcs.CONCUR.2025.36},
  annote =	{Keywords: probabilistic bisimilarity distance, labelled Markov chain, game, policy, explainability}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2025.3
Terminal Coalgebras for Finitary Functors

Authors: Jiří Adámek, Stefan Milius, and Lawrence S. Moss

Published in: LIPIcs, Volume 342, 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)

Abstract
We present a result that implies that an endofunctor on a category has a terminal coalgebra obtainable as a countable limit of its terminal-coalgebra sequence. It holds for finitary endofunctors preserving nonempty binary intersections on locally finitely presentable categories, assuming that the posets of strong quotients and subobjects of every finitely presentable object satisfy the descending chain condition. This allows one to adapt finiteness arguments that were originally advanced by Worrell concerning terminal coalgebras for finitary set functors. Examples include the categories of sets, posets, vector spaces, graphs, and nominal sets. A similar argument is presented for the category of metric spaces (although it is not locally finitely presentable).
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Jiří Adámek, Stefan Milius, and Lawrence S. Moss. Terminal Coalgebras for Finitary Functors. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{adamek_et_al:LIPIcs.CALCO.2025.3,
  author =	{Ad\'{a}mek, Ji\v{r}{\'\i} and Milius, Stefan and Moss, Lawrence S.},
  title =	{{Terminal Coalgebras for Finitary Functors}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{3:1--3:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-383-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{342},
  editor =	{C\^{i}rstea, Corina and Knapp, Alexander},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2025.3},
  URN =		{urn:nbn:de:0030-drops-235623},
  doi =		{10.4230/LIPIcs.CALCO.2025.3},
  annote =	{Keywords: terminal coalgebra, countable iteration, descending chain condition}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.15
On the Metric Nature of (Differential) Logical Relations

Authors: Ugo Dal Lago, Naohiko Hoshino, and Paolo Pistone

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Differential logical relations are a method to measure distances between higher-order programs. They differ from standard methods based on program metrics in that differences between functional programs are themselves functions, relating errors in input with errors in output, this way providing a more fine grained, contextual, information. The aim of this paper is to clarify the metric nature of differential logical relations. While previous work has shown that these do not give rise, in general, to (quasi-)metric spaces nor to partial metric spaces, we show that the distance functions arising from such relations, that we call quasi-quasi-metrics, can be related to both quasi-metrics and partial metrics, the latter being also captured by suitable relational definitions. Moreover, we exploit such connections to deduce some new compositional reasoning principles for program differences.
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Ugo Dal Lago, Naohiko Hoshino, and Paolo Pistone. On the Metric Nature of (Differential) Logical Relations. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 15:1-15:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dallago_et_al:LIPIcs.FSCD.2025.15,
  author =	{Dal Lago, Ugo and Hoshino, Naohiko and Pistone, Paolo},
  title =	{{On the Metric Nature of (Differential) Logical Relations}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{15:1--15:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.15},
  URN =		{urn:nbn:de:0030-drops-236300},
  doi =		{10.4230/LIPIcs.FSCD.2025.15},
  annote =	{Keywords: Differential Logical Relations, Quantales, Quasi-Metrics, Partial Metrics}
}
Document
DOI: 10.4230/DagRep.14.10.58
Behavioural Metrics and Quantitative Logics (Dagstuhl Seminar 24432)

Authors: Barbara König, Radu Mardare, Prakash Panangaden, Jurriaan Rot, and Florence Clerc

Published in: Dagstuhl Reports, Volume 14, Issue 10 (2025)

Abstract
This report documents the program and the outcome of Dagstuhl Seminar "Behavioural Metrics and Quantitative Logics" (24432). Behavioural metrics and quantitative logics specify quantitative aspects of systems. A metric measures how far apart two systems are in their behaviour while a quantititative logic evaluates the degree to which a state satisfies a formula. They are often intimately connected via a Hennessy-Milner theorem stating that the distance induced by a quantitative logic coincides with behavioural distance. There are various applications in model-checking, differential privacy, hybrid systems and learning. Several challenges in this area have been identified: studying suitable metrics and their corresponding logics, generalizing to the setting of coalgebras by parameterizing the branching type of the system under consideration, developing methods of quantitative algebraic reasoning, finding efficient methods for computing behavioural methods. This Dagstuhl Seminar provided a forum to researchers working in this area, to discuss the state-of-the-art and further developments, and in particular address applications in various domains.
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Barbara König, Radu Mardare, Prakash Panangaden, Jurriaan Rot, and Florence Clerc. Behavioural Metrics and Quantitative Logics (Dagstuhl Seminar 24432). In Dagstuhl Reports, Volume 14, Issue 10, pp. 58-75, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{konig_et_al:DagRep.14.10.58,
  author =	{K\"{o}nig, Barbara and Mardare, Radu and Panangaden, Prakash and Rot, Jurriaan and Clerc, Florence},
  title =	{{Behavioural Metrics and Quantitative Logics (Dagstuhl Seminar 24432)}},
  pages =	{58--75},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2025},
  volume =	{14},
  number =	{10},
  editor =	{K\"{o}nig, Barbara and Mardare, Radu and Panangaden, Prakash and Rot, Jurriaan and Clerc, Florence},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.14.10.58},
  URN =		{urn:nbn:de:0030-drops-230222},
  doi =		{10.4230/DagRep.14.10.58},
  annote =	{Keywords: Behavioural metrics, quantitative equational reasoning, quantitative logics}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.33
Quantitative Graded Semantics and Spectra of Behavioural Metrics

Authors: Jonas Forster, Lutz Schröder, Paul Wild, Harsh Beohar, Sebastian Gurke, Barbara König, and Karla Messing

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
Behavioural metrics provide a quantitative refinement of classical two-valued behavioural equivalences on systems with quantitative data, such as metric or probabilistic transition systems. In analogy to the linear-time/ branching-time spectrum of two-valued behavioural equivalences on transition systems, behavioural metrics vary in granularity, and are often characterized by fragments of suitable modal logics. In the latter respect, the quantitative case is, however, more involved than the two-valued one; in fact, we show that probabilistic metric trace distance cannot be characterized by any compositionally defined modal logic with unary modalities. We go on to provide a unifying treatment of spectra of behavioural metrics in the emerging framework of graded monads, working in coalgebraic generality, that is, parametrically in the system type. In the ensuing development of quantitative graded semantics, we introduce algebraic presentations of graded monads on the category of metric spaces. Moreover, we provide a general criterion for a given real-valued modal logic to characterize a given behavioural distance. As a case study, we apply this criterion to obtain a new characteristic modal logic for trace distance in fuzzy metric transition systems.
Cite as

Jonas Forster, Lutz Schröder, Paul Wild, Harsh Beohar, Sebastian Gurke, Barbara König, and Karla Messing. Quantitative Graded Semantics and Spectra of Behavioural Metrics. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{forster_et_al:LIPIcs.CSL.2025.33,
  author =	{Forster, Jonas and Schr\"{o}der, Lutz and Wild, Paul and Beohar, Harsh and Gurke, Sebastian and K\"{o}nig, Barbara and Messing, Karla},
  title =	{{Quantitative Graded Semantics and Spectra of Behavioural Metrics}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{33:1--33:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.33},
  URN =		{urn:nbn:de:0030-drops-227907},
  doi =		{10.4230/LIPIcs.CSL.2025.33},
  annote =	{Keywords: transition systems, modal logics, coalgebras, behavioural metrics}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.34
The Lambda Calculus Is Quantifiable

Authors: Valentin Maestracci and Paolo Pistone

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
In this paper we introduce several quantitative methods for the lambda-calculus based on partial metrics, a well-studied variant of standard metric spaces that have been used to metrize non-Hausdorff topologies, like those arising from Scott domains. First, we study quantitative variants, based on program distances, of sensible equational theories for the λ-calculus, like those arising from Böhm trees and from the contextual preorder. Then, we introduce applicative distances capturing higher-order Scott topologies, including reflexive objects like the D_∞ model. Finally, we provide a quantitative insight on the well-known connection between the Böhm tree of a λ-term and its Taylor expansion, by showing that the latter can be presented as an isometric transformation.
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Valentin Maestracci and Paolo Pistone. The Lambda Calculus Is Quantifiable. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 34:1-34:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{maestracci_et_al:LIPIcs.CSL.2025.34,
  author =	{Maestracci, Valentin and Pistone, Paolo},
  title =	{{The Lambda Calculus Is Quantifiable}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{34:1--34:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.34},
  URN =		{urn:nbn:de:0030-drops-227911},
  doi =		{10.4230/LIPIcs.CSL.2025.34},
  annote =	{Keywords: Lambda-calculus, Scott semantics, Partial metric spaces, B\"{o}hm trees, Taylor expansion}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.30
A Complete Inference System for Probabilistic Infinite Trace Equivalence

Authors: Corina Cîrstea, Lawrence S. Moss, Victoria Noquez, Todd Schmid, Alexandra Silva, and Ana Sokolova

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
We present the first sound and complete axiomatization of infinite trace semantics for generative probabilistic transition systems. Our approach is categorical, and we build on recent results on proper functors over convex sets. At the core of our proof is a characterization of infinite traces as the final coalgebra of a functor over convex algebras. Somewhat surprisingly, our axiomatization of infinite trace semantics coincides with that of finite trace semantics, even though the techniques used in the completeness proof are significantly different.
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Corina Cîrstea, Lawrence S. Moss, Victoria Noquez, Todd Schmid, Alexandra Silva, and Ana Sokolova. A Complete Inference System for Probabilistic Infinite Trace Equivalence. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 30:1-30:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cirstea_et_al:LIPIcs.CSL.2025.30,
  author =	{C\^{i}rstea, Corina and Moss, Lawrence S. and Noquez, Victoria and Schmid, Todd and Silva, Alexandra and Sokolova, Ana},
  title =	{{A Complete Inference System for Probabilistic Infinite Trace Equivalence}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{30:1--30:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.30},
  URN =		{urn:nbn:de:0030-drops-227870},
  doi =		{10.4230/LIPIcs.CSL.2025.30},
  annote =	{Keywords: Coalgebra, infinite trace, semantics, logic, convex sets}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.29
Correspondences Between Codensity and Coupling-Based Liftings, a Practical Approach

Authors: Samuel Humeau, Daniela Petrisan, and Jurriaan Rot

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
The Kantorovich distance is a widely used metric between probability distributions. The Kantorovich-Rubinstein duality states that it can be defined in two equivalent ways: as a supremum, based on non-expansive functions into [0,1], and as an infimum, based on probabilistic couplings. Orthogonally, there are categorical generalisations of both presentations proposed in the literature, in the form of codensity liftings and what we refer to as coupling-based liftings. Both lift endofunctors on the category Set of sets and functions to that of pseudometric spaces, and both are parameterised by modalities from coalgebraic modal logic. A generalisation of the Kantorovich-Rubinstein duality has been more nebulous - it is known not to work in some cases. In this paper we propose a compositional approach for obtaining such generalised dualities for a class of functors, which is closed under coproducts and products. Our approach is based on an explicit construction of modalities and also applies to and extends known cases such as that of the powerset functor.
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Samuel Humeau, Daniela Petrisan, and Jurriaan Rot. Correspondences Between Codensity and Coupling-Based Liftings, a Practical Approach. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{humeau_et_al:LIPIcs.CSL.2025.29,
  author =	{Humeau, Samuel and Petrisan, Daniela and Rot, Jurriaan},
  title =	{{Correspondences Between Codensity and Coupling-Based Liftings, a Practical Approach}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.29},
  URN =		{urn:nbn:de:0030-drops-227861},
  doi =		{10.4230/LIPIcs.CSL.2025.29},
  annote =	{Keywords: Kantorovich distance, behavioural metrics, Kantorovich-Rubinstein duality, functor liftings}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2021.7
Tensor of Quantitative Equational Theories

Authors: Giorgio Bacci, Radu Mardare, Prakash Panangaden, and Gordon Plotkin

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

Abstract
We develop a theory for the commutative combination of quantitative effects, their tensor, given as a combination of quantitative equational theories that imposes mutual commutation of the operations from each theory. As such, it extends the sum of two theories, which is just their unrestrained combination. Tensors of theories arise in several contexts; in particular, in the semantics of programming languages, the monad transformer for global state is given by a tensor. We show that under certain assumptions on the quantitative theories the free monad that arises from the tensor of two theories is the categorical tensor of the free monads on the theories. As an application, we provide the first algebraic axiomatizations of labelled Markov processes and Markov decision processes. Apart from the intrinsic interest in the axiomatizations, it is pleasing they are obtained compositionally by means of the sum and tensor of simpler quantitative equational theories.
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Giorgio Bacci, Radu Mardare, Prakash Panangaden, and Gordon Plotkin. Tensor of Quantitative Equational Theories. In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bacci_et_al:LIPIcs.CALCO.2021.7,
  author =	{Bacci, Giorgio and Mardare, Radu and Panangaden, Prakash and Plotkin, Gordon},
  title =	{{Tensor of Quantitative Equational Theories}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{7:1--7:17},
  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.2021.7},
  URN =		{urn:nbn:de:0030-drops-153628},
  doi =		{10.4230/LIPIcs.CALCO.2021.7},
  annote =	{Keywords: Quantitative equational theories, Tensor, Monads, Quantitative Effects}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2019.9
Computing Probabilistic Bisimilarity Distances for Probabilistic Automata

Authors: Giorgio Bacci, Giovanni Bacci, Kim G. Larsen, Radu Mardare, Qiyi Tang, and Franck van Breugel

Published in: LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)

Abstract
The probabilistic bisimilarity distance of Deng et al. has been proposed as a robust quantitative generalization of Segala and Lynch’s probabilistic bisimilarity for probabilistic automata. In this paper, we present a novel characterization of the bisimilarity distance as the solution of a simple stochastic game. The characterization gives us an algorithm to compute the distances by applying Condon’s simple policy iteration on these games. The correctness of Condon’s approach, however, relies on the assumption that the games are stopping. Our games may be non-stopping in general, yet we are able to prove termination for this extended class of games. Already other algorithms have been proposed in the literature to compute these distances, with complexity in UP cap coUP and PPAD. Despite the theoretical relevance, these algorithms are inefficient in practice. To the best of our knowledge, our algorithm is the first practical solution. In the proofs of all the above-mentioned results, an alternative presentation of the Hausdorff distance due to Mémoli plays a central rôle.
Cite as

Giorgio Bacci, Giovanni Bacci, Kim G. Larsen, Radu Mardare, Qiyi Tang, and Franck van Breugel. Computing Probabilistic Bisimilarity Distances for Probabilistic Automata. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bacci_et_al:LIPIcs.CONCUR.2019.9,
  author =	{Bacci, Giorgio and Bacci, Giovanni and Larsen, Kim G. and Mardare, Radu and Tang, Qiyi and van Breugel, Franck},
  title =	{{Computing Probabilistic Bisimilarity Distances for Probabilistic Automata}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Fokkink, Wan and van Glabbeek, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.9},
  URN =		{urn:nbn:de:0030-drops-109119},
  doi =		{10.4230/LIPIcs.CONCUR.2019.9},
  annote =	{Keywords: Probabilistic automata, Behavioural metrics, Simple stochastic games, Simple policy iteration algorithm}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.104
On the Metric-Based Approximate Minimization of Markov Chains

Authors: Giovanni Bacci, Giorgio Bacci, Kim G. Larsen, and Radu Mardare

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
We address the behavioral metric-based approximate minimization problem of Markov Chains (MCs), i.e., given a finite MC and a positive integer k, we are interested in finding a k-state MC of minimal distance to the original. By considering as metric the bisimilarity distance of Desharnais at al., we show that optimal approximations always exist; show that the problem can be solved as a bilinear program; and prove that its threshold problem is in PSPACE and NP-hard. Finally, we present an approach inspired by expectation maximization techniques that provides suboptimal solutions. Experiments suggest that our method gives a practical approach that outperforms the bilinear program implementation run on state-of-the-art bilinear solvers.
Cite as

Giovanni Bacci, Giorgio Bacci, Kim G. Larsen, and Radu Mardare. On the Metric-Based Approximate Minimization of Markov Chains. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 104:1-104:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bacci_et_al:LIPIcs.ICALP.2017.104,
  author =	{Bacci, Giovanni and Bacci, Giorgio and Larsen, Kim G. and Mardare, Radu},
  title =	{{On the Metric-Based Approximate Minimization of Markov Chains}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{104:1--104:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.104},
  URN =		{urn:nbn:de:0030-drops-73675},
  doi =		{10.4230/LIPIcs.ICALP.2017.104},
  annote =	{Keywords: Behavioral distances, Probabilistic Models, Automata Minimization}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2016.25
Probabilistic Mu-Calculus: Decidability and Complete Axiomatization

Authors: Kim G. Larsen, Radu Mardare, and Bingtian Xue

Published in: LIPIcs, Volume 65, 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)

Abstract
We introduce a version of the probabilistic mu-calculus (PMC) built on top of a probabilistic modal logic that allows encoding n-ary inequational conditions on transition probabilities. PMC extends previously studied calculi and we prove that, despite its expressiveness, it enjoys a series of good meta-properties. Firstly, we prove the decidability of satisfiability checking by establishing the small model property. An algorithm for deciding the satisfiability problem is developed. As a second major result, we provide a complete axiomatization for the alternation-free fragment of PMC. The completeness proof is innovative in many aspects combining various techniques from topology and model theory.
Cite as

Kim G. Larsen, Radu Mardare, and Bingtian Xue. Probabilistic Mu-Calculus: Decidability and Complete Axiomatization. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 25:1-25:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{larsen_et_al:LIPIcs.FSTTCS.2016.25,
  author =	{Larsen, Kim G. and Mardare, Radu and Xue, Bingtian},
  title =	{{Probabilistic Mu-Calculus: Decidability and Complete Axiomatization}},
  booktitle =	{36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)},
  pages =	{25:1--25:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-027-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{65},
  editor =	{Lal, Akash and Akshay, S. and Saurabh, Saket and Sen, Sandeep},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2016.25},
  URN =		{urn:nbn:de:0030-drops-68607},
  doi =		{10.4230/LIPIcs.FSTTCS.2016.25},
  annote =	{Keywords: Markov process, probabilistic modal mu-calculus, n-ary (in-)equational modalities, satisfiability, axiomatization}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2016.21
Complete Axiomatization for the Bisimilarity Distance on Markov Chains

Authors: Giorgio Bacci, Giovanni Bacci, Kim G. Larsen, and Radu Mardare

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

Abstract
In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS'16) that uses equality relations t =_e s indexed by rationals, expressing that "t is approximately equal to s up to an error e". Notably, our quantitative deductive system extends in a natural way the equational system for probabilistic bisimilarity given by Stark and Smolka by introducing an axiom for dealing with the Kantorovich distance between probability distributions.
Cite as

Giorgio Bacci, Giovanni Bacci, Kim G. Larsen, and Radu Mardare. Complete Axiomatization for the Bisimilarity Distance on Markov Chains. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 21:1-21:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{bacci_et_al:LIPIcs.CONCUR.2016.21,
  author =	{Bacci, Giorgio and Bacci, Giovanni and G. Larsen, Kim and Mardare, Radu},
  title =	{{Complete Axiomatization for the Bisimilarity Distance on Markov Chains}},
  booktitle =	{27th International Conference on Concurrency Theory (CONCUR 2016)},
  pages =	{21:1--21:14},
  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.2016.21},
  URN =		{urn:nbn:de:0030-drops-61569},
  doi =		{10.4230/LIPIcs.CONCUR.2016.21},
  annote =	{Keywords: Markov chains, Behavioral distances, Axiomatization}
}
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