23 Search Results for "Petrisan, Daniela"

Document
DOI: 10.4230/LIPIcs.STACS.2026.65
Demystifying Codensity Monads via Duality

Authors: Fabian Lenke, Nico Wittrock, Stefan Milius, and Henning Urbat

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Codensity monads provide a universal method to generate complex monads from simple functors. Recently, a wide range of important monads in logic, denotational semantics, and probabilistic computation, such as several incarnations of the ultrafilter monad, the Vietoris monad, and the Giry monad, have been presented as codensity monads, using complex arguments. We propose a unifying categorical approach to codensity presentations of monads, based on the idea of relating the presenting functor to a dense functor via a suitable duality between categories. We prove a general presentation result applying to every such situation and demonstrate that most codensity presentations known in the literature emerge from this strikingly simple duality-based setup, drastically alleviating the complexity of their proofs and in many cases completely reducing them to standard duality results. Additionally, we derive a number of novel codensity presentations using our framework, including the first non-trivial codensity presentations for the filter monads on sets and topological spaces, the lower Vietoris monad on topological spaces, and the expectation monad on sets.
Cite as

Fabian Lenke, Nico Wittrock, Stefan Milius, and Henning Urbat. Demystifying Codensity Monads via Duality. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 65:1-65:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{lenke_et_al:LIPIcs.STACS.2026.65,
  author =	{Lenke, Fabian and Wittrock, Nico and Milius, Stefan and Urbat, Henning},
  title =	{{Demystifying Codensity Monads via Duality}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{65:1--65:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.65},
  URN =		{urn:nbn:de:0030-drops-255549},
  doi =		{10.4230/LIPIcs.STACS.2026.65},
  annote =	{Keywords: Codensity, Monad, Duality}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.26
ε-Distance via Lévy-Prokhorov Lifting

Authors: Josée Desharnais and Ana Sokolova

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
The most studied and accepted pseudometric for probabilistic processes is one based on the Kantorovich distance between distributions. It comes with many theoretical and motivating results, in particular it is the fixpoint of a given functional and defines a functor on (complete) pseudometric spaces. It is also the foundation for a categorical lifting of pseudometrics. Other notions of behavioural pseudometrics have also been proposed, one of them (ε-distance) based on ε-bisimulation. ε-Distance has the advantages that it is intuitively easy to understand, it relates systems that are conceptually close (for example, an imperfect implementation is close to its specification), and it comes equipped with a natural notion of ε-coupling. Finally, this distance is easy to compute. We show that ε-distance is also the greatest fixpoint of a functional and provides a functor. The latter is obtained by replacing the Kantorovich distance in the lifting functor with the Lévy-Prokhorov distance. In addition, we show that ε-couplings and ε-bisimulations have an appealing coalgebraic characterization.
Cite as

Josée Desharnais and Ana Sokolova. ε-Distance via Lévy-Prokhorov Lifting. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 26:1-26:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{desharnais_et_al:LIPIcs.CSL.2026.26,
  author =	{Desharnais, Jos\'{e}e and Sokolova, Ana},
  title =	{{\epsilon-Distance via L\'{e}vy-Prokhorov Lifting}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{26:1--26:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.26},
  URN =		{urn:nbn:de:0030-drops-254506},
  doi =		{10.4230/LIPIcs.CSL.2026.26},
  annote =	{Keywords: L\'{e}vy-Prokhorov metric, behavioural distance, epsilon-bisimulation, reactive probabilistic transition systems, discrete labelled Markov processes, coalgebraic epsilon-(bi)simulation}
}
Document
DOI: 10.4230/DagRep.15.3.177
Categories for Automata and Language Theory (Dagstuhl Seminar 25141)

Authors: Achim Blumensath, Mikołaj Bojańczyk, Bartek Klin, and Daniela Petrişan

Published in: Dagstuhl Reports, Volume 15, Issue 3 (2025)

Abstract
Categorical methods have a long history in automata and language theory, but a coherent theory has started to emerge only in recent years. The abstract viewpoint of category theory can provide a unifying perspective on various forms of automata; it can make it easier to bootstrap a theory in a new setting; and it provides conceptual clarity regarding which aspects and properties are fundamental and which are only coincidental. Due to being in its early stages, the field is currently still divided into several different communities with little connections between them. One of the central aims of the Dagstuhl Seminar "Categories for Automata and Language Theory" (25141) was to enhance communication between automata theory and category theory communities. To this end, the seminar brought together researchers from both areas and included introductory tutorials designed to provide common ground and help participants better understand each other’s approach and terminology. The following key topics were explored during the seminar: - Categorical unification of language theory, either via the theory of monads, or via the category of MSO-transductions and their composition; - Coalgebraic methods and their applications to automata theory, to infinite trace semantics and connection to bisimulation-invariant fragments of logics; - Functorial automata and generic algorithms therein; - Fibrational and monoidal perspectives on language theory; - Higher-order automata and profinite lambda-calculus.
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Achim Blumensath, Mikołaj Bojańczyk, Bartek Klin, and Daniela Petrişan. Categories for Automata and Language Theory (Dagstuhl Seminar 25141). In Dagstuhl Reports, Volume 15, Issue 3, pp. 177-200, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{blumensath_et_al:DagRep.15.3.177,
  author =	{Blumensath, Achim and Boja\'{n}czyk, Miko{\l}aj and Klin, Bartek and Petri\c{s}an, Daniela},
  title =	{{Categories for Automata and Language Theory (Dagstuhl Seminar 25141)}},
  pages =	{177--200},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2025},
  volume =	{15},
  number =	{3},
  editor =	{Blumensath, Achim and Boja\'{n}czyk, Miko{\l}aj and Klin, Bartek and Petri\c{s}an, Daniela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.15.3.177},
  URN =		{urn:nbn:de:0030-drops-248949},
  doi =		{10.4230/DagRep.15.3.177},
  annote =	{Keywords: categorical automata theory, automata theory, category theory, monads}
}
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.
Cite as

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
(Co)algebraic pearl
DOI: 10.4230/LIPIcs.CALCO.2025.16
Active Learning of Upward-Closed Sets of Words ((Co)algebraic pearl)

Authors: Quentin Aristote

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

Abstract
We give a new proof of a result from well quasi-order theory on the computability of bases for upwards-closed sets of words. This new proof is based on Angluin’s L* algorithm, that learns an automaton from a minimally adequate teacher. This relates in particular two results from the 1980s: Angluin’s L* algorithm, and a result from Valk and Jantzen on the computability of bases for upwards-closed sets of tuples of integers. Along the way, we describe an algorithm for learning quasi-ordered automata from a minimally adequate teacher, and extend a generalization of Valk and Jantzen’s result, encompassing both words and integers, to finitely generated monoids.
Cite as

Quentin Aristote. Active Learning of Upward-Closed Sets of Words ((Co)algebraic pearl). In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 16:1-16:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aristote:LIPIcs.CALCO.2025.16,
  author =	{Aristote, Quentin},
  title =	{{Active Learning of Upward-Closed Sets of Words}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{16:1--16:12},
  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.2025.16},
  URN =		{urn:nbn:de:0030-drops-235751},
  doi =		{10.4230/LIPIcs.CALCO.2025.16},
  annote =	{Keywords: active learning, well quasi-orders, Valk-Jantzen lemma, piecewise-testable languages, monoids}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2025.13
Expressivity of Bisimulation Pseudometrics over Analytic State Spaces

Authors: Daniel Luckhardt, Harsh Beohar, and Clemens Kupke

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

Abstract
A Markov decision process (MDP) is a state-based dynamical system capable of describing probabilistic behaviour with rewards. In this paper, we view MDPs as coalgebras living in the category of analytic spaces, a very general class of measurable spaces. Note that analytic spaces were already studied in the literature on labelled Markov processes and bisimulation relations. Our results are twofold. First, we define bisimulation pseudometrics over such coalgebras using the framework of fibrations. Second, we develop a quantitative modal logic for such coalgebras and prove a quantitative form of Hennessy-Milner theorem in this new setting stating that the bisimulation pseudometric corresponds to the logical distance induced by modal formulae.
Cite as

Daniel Luckhardt, Harsh Beohar, and Clemens Kupke. Expressivity of Bisimulation Pseudometrics over Analytic State Spaces. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 13:1-13:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{luckhardt_et_al:LIPIcs.CALCO.2025.13,
  author =	{Luckhardt, Daniel and Beohar, Harsh and Kupke, Clemens},
  title =	{{Expressivity of Bisimulation Pseudometrics over Analytic State Spaces}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{13:1--13:23},
  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.2025.13},
  URN =		{urn:nbn:de:0030-drops-235727},
  doi =		{10.4230/LIPIcs.CALCO.2025.13},
  annote =	{Keywords: Markov decision process, quantitative Hennessy-Milner theorem}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2025.12
Cancellative Convex Semilattices

Authors: Ana Sokolova and Harald Woracek

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

Abstract
Convex semilattices are algebras that are at the same time a convex algebra and a semilattice, together with a distributivity axiom. These algebras have attracted some attention in the last years as suitable algebras for probability and nondeterminism, in particular by being the Eilenberg-Moore algebras of the nonempty finitely-generated convex subsets of the distributions monad. A convex semilattice is cancellative if the underlying convex algebra is cancellative. Cancellative convex algebras have been characterized by M. H. Stone and by H. Kneser: A convex algebra is cancellative if and only if it is isomorphic to a convex subset of a vector space (with canonical convex algebra operations). We prove an analogous theorem for convex semilattices: A convex semilattice is cancellative if and only if it is isomorphic to a convex subset of a Riesz space, i.e., a lattice-ordered vector space (with canonical convex semilattice operations).
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Ana Sokolova and Harald Woracek. Cancellative Convex Semilattices. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sokolova_et_al:LIPIcs.CALCO.2025.12,
  author =	{Sokolova, Ana and Woracek, Harald},
  title =	{{Cancellative Convex Semilattices}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{12:1--12:15},
  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.2025.12},
  URN =		{urn:nbn:de:0030-drops-235714},
  doi =		{10.4230/LIPIcs.CALCO.2025.12},
  annote =	{Keywords: convex semilattice, cancellativity, Riesz space}
}
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).
Cite as

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
Invited Talk
DOI: 10.4230/LIPIcs.CALCO.2025.2
Logic Enriched over a Quantale (Invited Talk)

Authors: Alexander Kurz

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

Abstract
Many-valued logics have a long history in mathematical logic as well as in applications to the semantics of programming languages and to engineering more generally. Typically these logics are rich with features motivated by the particular applications they stem from. In his 1973 article "Metric Spaces, Generalized Logic, and Closed Categories", Lawvere argued that any quantale Ω gives rise to a generalized Ω-valued logic that has as its models the categories enriched over the quantale. This suggests developing a uniform framework for many-valued logics parameterized in a quantale. In this talk we will review some previous and ongoing work in that direction. In particular, we will address (not necessarily answer) the following questions. - If we take as our starting point, generalizing from 2-valued lattice logic, a logical language that comprises not only meets and joins (limits and colimits) but also tensor and power (weighted limits and colimits), what laws do these operations satisfy? - This question can be investigated for different types of semantics, generalizing the set-theoretic and the polarity-based semantics known from the 2-valued setting. - Which additional properties obtain if the quantale is integral or commutative or finite or distributive, etc? - On the other hand, quantale logics can also be investigated from a purely proof theoretic point of view, leading us to consider sequent calculi with turnstiles ⊢_ω labelled by elements ω ∈ Ω. - As Galatos and Jipsen showed, there are 1662 "Residuated Lattices of Size up to 6". Each of them generates a different and potentially interesting logic. - The adjunction Ω^-⊣ Ω^-:Ω-cat^op → Ω-cat exists for any quantale Ω. What is the logic enshrined in the monad of that adjunction? How far can one extend this to a theory of Stone duality for quantale logics parametric in the quantale? - The Dedekind-MacNeille completion generalizes to quantale categories. Similarly, the theory of canonical extensions originating with Jonsson and Tarski (and important for completeness proofs of modal logics) can be extended to quantale logics. - Since the discrete functor Set → Ω-cat is dense in the sense of Kelly, set-functors (equipped with an Ω-cat structure or not) can be extended to quantale categories via enriched left Kan extensions. This gives rise to a uniform variety of type constructors (endofunctors) on quantale categories parameterised by the quantale. - Each endofunctor on Ω-cat gives rise to a category of coalgebras with their own notion of behavioural equivalence. How many of the existing notions of many-valued (probabilistic, metric, fuzzy, etc) bisimulation can be accounted for in this uniform framework? - Morphism between quantales gives rise to change-of-base principles between categories of (co)algebras. Which transfer principles can be obtained from a systematic investigation of change of base for quantale categories? - Exploiting the duality of coalgebras (as models of computation) and algebras (as modal logics), which general logical theory of computation arises from putting the items in this list together?
Cite as

Alexander Kurz. Logic Enriched over a Quantale (Invited Talk). In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kurz:LIPIcs.CALCO.2025.2,
  author =	{Kurz, Alexander},
  title =	{{Logic Enriched over a Quantale}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{2:1--2:1},
  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.2025.2},
  URN =		{urn:nbn:de:0030-drops-235609},
  doi =		{10.4230/LIPIcs.CALCO.2025.2},
  annote =	{Keywords: Modal Logic, Coalgebra, Enriched Category Theory}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.165
Algebraic Language Theory with Effects

Authors: Fabian Lenke, Stefan Milius, Henning Urbat, and Thorsten Wißmann

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Regular languages - the languages accepted by deterministic finite automata - are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we generalize the correspondence between automata and monoids to automata with generic computational effects given by a monad, providing the foundations of an effectful algebraic language theory. We show that, under suitable conditions on the monad, a language is computable by an effectful automaton precisely when it is recognizable by (1) an effectful monoid morphism into an effect-free finite monoid, and (2) a monoid morphism into a monad-monoid bialgebra whose carrier is a finitely generated algebra for the monad, the former mode of recognition being conceptually completely new. Our prime application is a novel algebraic approach to languages computed by probabilistic finite automata. Additionally, we derive new algebraic characterizations for nondeterministic probabilistic finite automata and for weighted finite automata over unrestricted semirings, generalizing previous results on weighted algebraic recognition over commutative rings.
Cite as

Fabian Lenke, Stefan Milius, Henning Urbat, and Thorsten Wißmann. Algebraic Language Theory with Effects. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 165:1-165:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lenke_et_al:LIPIcs.ICALP.2025.165,
  author =	{Lenke, Fabian and Milius, Stefan and Urbat, Henning and Wi{\ss}mann, Thorsten},
  title =	{{Algebraic Language Theory with Effects}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{165:1--165:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.165},
  URN =		{urn:nbn:de:0030-drops-235423},
  doi =		{10.4230/LIPIcs.ICALP.2025.165},
  annote =	{Keywords: Automaton, Monoid, Monad, Effect, Algebraic language theory}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.10
Monotone Weak Distributive Laws over the Lifted Powerset Monad in Categories of Algebras

Authors: Quentin Aristote

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
In both the category of sets and the category of compact Hausdorff spaces, there is a monotone weak distributive law that combines two layers of non-determinism. Noticing the similarity between these two laws, we study whether the latter can be obtained automatically as a weak lifting of the former. This holds partially, but does not generalize to other categories of algebras. We then characterize when exactly monotone weak distributive laws over powerset monads in categories of algebras exist, on the one hand exhibiting a law combining probabilities and non-determinism in compact Hausdorff spaces and showing on the other hand that such laws do not exist in a lot of other cases.
Cite as

Quentin Aristote. Monotone Weak Distributive Laws over the Lifted Powerset Monad in Categories of Algebras. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aristote:LIPIcs.STACS.2025.10,
  author =	{Aristote, Quentin},
  title =	{{Monotone Weak Distributive Laws over the Lifted Powerset Monad in Categories of Algebras}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.10},
  URN =		{urn:nbn:de:0030-drops-228356},
  doi =		{10.4230/LIPIcs.STACS.2025.10},
  annote =	{Keywords: weak distributive law, weak extension, weak lifting, iterated distributive law, Yang-Baxter equation, powerset monad, Vietoris monad, Radon monad, Eilenberg-Moore category, regular category, relational extension}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.40
Identity-Preserving Lax Extensions and Where to Find Them

Authors: Sergey Goncharov, Dirk Hofmann, Pedro Nora, Lutz Schröder, and Paul Wild

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
Generic notions of bisimulation for various types of systems (nondeterministic, probabilistic, weighted etc.) rely on identity-preserving (normal) lax extensions of the functor encapsulating the system type, in the paradigm of universal coalgebra. It is known that preservation of weak pullbacks is a sufficient condition for a functor to admit a normal lax extension (the Barr extension, which in fact is then even strict); in the converse direction, nothing is currently known about necessary (weak) pullback preservation conditions for the existence of normal lax extensions. In the present work, we narrow this gap by showing on the one hand that functors admitting a normal lax extension preserve 1/4-iso pullbacks, i.e. pullbacks in which at least one of the projections is an isomorphism. On the other hand, we give sufficient conditions, showing that a functor admits a normal lax extension if it weakly preserves either 1/4-iso pullbacks and 4/4-epi pullbacks (i.e. pullbacks in which all morphisms are epic) or inverse images. We apply these criteria to concrete examples, in particular to functors modelling neighbourhood systems and weighted systems.
Cite as

Sergey Goncharov, Dirk Hofmann, Pedro Nora, Lutz Schröder, and Paul Wild. Identity-Preserving Lax Extensions and Where to Find Them. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 40:1-40:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{goncharov_et_al:LIPIcs.STACS.2025.40,
  author =	{Goncharov, Sergey and Hofmann, Dirk and Nora, Pedro and Schr\"{o}der, Lutz and Wild, Paul},
  title =	{{Identity-Preserving Lax Extensions and Where to Find Them}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{40:1--40:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.40},
  URN =		{urn:nbn:de:0030-drops-228665},
  doi =		{10.4230/LIPIcs.STACS.2025.40},
  annote =	{Keywords: (Bi-)simulations, lax extensions, modal logics, coalgebra}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.28
Strong Induction Is an Up-To Technique

Authors: Filippo Bonchi, Elena Di Lavore, and Anna Ricci

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

Abstract
Up-to techniques are enhancements of the coinduction proof principle which, in lattice theoretic terms, is the dual of induction. What is the dual of coinduction up-to? By means of duality, we illustrate a theory of induction up-to and we observe that an elementary proof technique, commonly known as strong induction, is an instance of induction up-to. We also show that, when generalising our theory from lattices to categories, one obtains an enhancement of the induction definition principle known in the literature as comonadic recursion.
Cite as

Filippo Bonchi, Elena Di Lavore, and Anna Ricci. Strong Induction Is an Up-To Technique. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 28:1-28:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonchi_et_al:LIPIcs.CSL.2025.28,
  author =	{Bonchi, Filippo and Di Lavore, Elena and Ricci, Anna},
  title =	{{Strong Induction Is an Up-To Technique}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{28:1--28:21},
  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.2025.28},
  URN =		{urn:nbn:de:0030-drops-227856},
  doi =		{10.4230/LIPIcs.CSL.2025.28},
  annote =	{Keywords: Induction, Coinduction, Up-to Techniques, Induction up-to, Lattices, Algebras}
}
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.
Cite as

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
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2021.132
Powerset-Like Monads Weakly Distribute over Themselves in Toposes and Compact Hausdorff Spaces

Authors: Alexandre Goy, Daniela Petrişan, and Marc Aiguier

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
The powerset monad on the category of sets does not distribute over itself. Nevertheless a weaker form of distributive law of the powerset monad over itself exists and it essentially stems from the canonical Egli-Milner extension of the powerset to the category of relations. On the other hand, any regular category yields a category of relations, and some regular categories also possess a powerset-like monad, as is the Vietoris monad on compact Hausdorff spaces. We derive the Egli-Milner extension in three different frameworks : sets, toposes, and compact Hausdorff spaces. We prove that it corresponds to a monotone weak distributive law in each case by showing that the multiplication extends to relations but the unit does not. We provide an application to coalgebraic determinization of alternating automata.
Cite as

Alexandre Goy, Daniela Petrişan, and Marc Aiguier. Powerset-Like Monads Weakly Distribute over Themselves in Toposes and Compact Hausdorff Spaces. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 132:1-132:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{goy_et_al:LIPIcs.ICALP.2021.132,
  author =	{Goy, Alexandre and Petri\c{s}an, Daniela and Aiguier, Marc},
  title =	{{Powerset-Like Monads Weakly Distribute over Themselves in Toposes and Compact Hausdorff Spaces}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{132:1--132:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.132},
  URN =		{urn:nbn:de:0030-drops-142016},
  doi =		{10.4230/LIPIcs.ICALP.2021.132},
  annote =	{Keywords: Egli-Milner relation, weak extension, weak distributive law, weak lifting, powerset monad, Vietoris monad, topos, alternating automaton, generalized determinization}
}
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