48 Search Results for "Baldan, Paolo"

Volume

LIPIcs, Volume 270

10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)

CALCO 2023, June 19-21, 2023, Indiana University Bloomington, IN, USA

Editors: Paolo Baldan and Valeria de Paiva

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
Invited Paper
DOI: 10.4230/LIPIcs.CSL.2026.3
Rational Lawvere Logic (Invited Paper)

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

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

Abstract
We study Rational Lawvere logic (RL). This logic is defined over the extended positive reals with an algebraic structure combining the Lawvere quantale (with the reversed order on the extended reals and a sum as tensor) and a multiplicative quantale (with the usual order on the extended reals and a multiplication as tensor); together they provide a semiring structure. The logic is designed for complex quantitative reasoning, including sequents expressing inequalities between rational functions over the extended positive reals. We give a deduction system and demonstrate its expressiveness by deriving a classical result from probability theory relating the Kantorovich and total variation distances. Our deductive system is complete for finitely axiomatizable theories. The proof of completeness relies on the Krivine-Stengle Positivstellensatz. We additionally provide complexity results for both RL and its affine fragment AL. We consider two decision problems: the satisfiability of a set of sequents and whether a sequent follows from a finite set of sequent. We show that both problems lie in PSPACE for RL, and we give sharper complexity bounds for AL: the first problem is NP-complete, while the second is co-NP-complete.
Cite as

Giorgio Bacci, Radu Mardare, Prakash Panangaden, and Gordon Plotkin. Rational Lawvere Logic (Invited Paper). In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 3:1-3:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bacci_et_al:LIPIcs.CSL.2026.3,
  author =	{Bacci, Giorgio and Mardare, Radu and Panangaden, Prakash and Plotkin, Gordon},
  title =	{{Rational Lawvere Logic}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{3:1--3:21},
  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.2026.3},
  URN =		{urn:nbn:de:0030-drops-254277},
  doi =		{10.4230/LIPIcs.CSL.2026.3},
  annote =	{Keywords: Quantitative reasoning, complete deductive system, Lawvere’s quantale}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.24
A Note on the Parameterised Complexity of Coverability in Vector Addition Systems

Authors: Michał Pilipczuk, Sylvain Schmitz, and Henry Sinclair-Banks

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
We investigate the parameterised complexity of the classic coverability problem for vector addition systems (VAS): V ⊆ ℤ^d, an initial configuration s ∈ ℕ^d, and a target configuration t ∈ ℕ^d, decide whether starting from s, one can iteratively add vectors from V to ultimately arrive at a configuration that is larger than or equal to t on every coordinate, while not observing any negative value on any coordinate along the way. We consider two natural parameters for the problem: the dimension d and the size of V, defined as the total bitsize of its encoding. We present several results charting the complexity of those two parameterisations, among which the highlight is that coverability for VAS parameterised by the dimension and with all the numbers in the input encoded in unary is complete for the class XNL under PL-reductions. We also discuss open problems in the topic, most notably the question about fixed-parameter tractability for the parameterisation by the size of V.
Cite as

Michał Pilipczuk, Sylvain Schmitz, and Henry Sinclair-Banks. A Note on the Parameterised Complexity of Coverability in Vector Addition Systems. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{pilipczuk_et_al:LIPIcs.IPEC.2025.24,
  author =	{Pilipczuk, Micha{\l} and Schmitz, Sylvain and Sinclair-Banks, Henry},
  title =	{{A Note on the Parameterised Complexity of Coverability in Vector Addition Systems}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{24:1--24:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.24},
  URN =		{urn:nbn:de:0030-drops-251563},
  doi =		{10.4230/LIPIcs.IPEC.2025.24},
  annote =	{Keywords: vector addition system, Petri net, parameterised complexity, coverability}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.8
Model Checking as Program Verification by Abstract Interpretation

Authors: Paolo Baldan, Roberto Bruni, Francesco Ranzato, and Diletta Rigo

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

Abstract
Abstract interpretation offers a powerful toolset for static analysis, tackling precision, complexity and state-explosion issues. In the literature, state partitioning abstractions based on (bi)simulation and property-preserving state relations have been successfully applied to abstract model checking. Here, we pursue a different track in which model checking is seen as an instance of program verification. To this purpose, we introduce a suitable language - called MOKA (for MOdel checking as abstract interpretation of 𝖪leene 𝖠lgebras) - which is used to encode temporal formulae as programs. In particular, we show that (universal fragments of) temporal logics, such as ACTL or, more generally, universal μ-calculus can be transformed into MOKA programs. Such programs return all and only the initial states which violate the formula. By applying abstract interpretation to MOKA programs, we pave the way for reusing more general abstractions than partitions as well as for tuning the precision of the abstraction to remove or avoid false alarms. We show how to perform model checking via a program logic that combines under-approximation and abstract interpretation analysis to avoid false alarms. The notion of locally complete abstraction is used to dynamically improve the analysis precision via counterexample-guided domain refinement.
Cite as

Paolo Baldan, Roberto Bruni, Francesco Ranzato, and Diletta Rigo. Model Checking as Program Verification by Abstract Interpretation. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{baldan_et_al:LIPIcs.CONCUR.2025.8,
  author =	{Baldan, Paolo and Bruni, Roberto and Ranzato, Francesco and Rigo, Diletta},
  title =	{{Model Checking as Program Verification by Abstract Interpretation}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{8:1--8:20},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-239583},
  doi =		{10.4230/LIPIcs.CONCUR.2025.8},
  annote =	{Keywords: ACTL, \mu-calculus, model checking, abstract interpretation, program analysis, local completeness, abstract interpretation repair, domain refinement, Kleene algebra with tests}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2025.9
Safety and Strong Completeness via Reducibility for Many-Valued Coalgebraic Dynamic Logics

Authors: Helle Hvid Hansen and Wolfgang Poiger

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

Abstract
We present a coalgebraic framework for studying generalisations of dynamic modal logics such as PDL and game logic in which both the propositions and the semantic structures can take values in an algebra 𝐀 of truth-degrees. More precisely, we work with coalgebraic modal logic via 𝐀-valued predicate liftings where 𝐀 is an FLew-algebra, and interpret actions (abstracting programs and games) as 𝖥-coalgebras where the functor 𝖥 represents some type of 𝐀-weighted system. We also allow combinations of crisp propositions with 𝐀-weighted systems and vice versa. We introduce coalgebra operations and tests, with a focus on operations which are reducible in the sense that modalities for composed actions can be reduced to compositions of modalities for the constituent actions. We prove that reducible operations are safe for bisimulation and behavioural equivalence, and prove a general strong completeness result, from which we obtain new strong completeness results for 𝟐-valued iteration-free PDL with 𝐀-valued accessibility relations when 𝐀 is a finite chain, and for many-valued iteration-free game logic with many-valued strategies based on finite Lukasiewicz logic.
Cite as

Helle Hvid Hansen and Wolfgang Poiger. Safety and Strong Completeness via Reducibility for Many-Valued Coalgebraic Dynamic Logics. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 9:1-9:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hansen_et_al:LIPIcs.CALCO.2025.9,
  author =	{Hansen, Helle Hvid and Poiger, Wolfgang},
  title =	{{Safety and Strong Completeness via Reducibility for Many-Valued Coalgebraic Dynamic Logics}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{9:1--9:23},
  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.2025.9},
  URN =		{urn:nbn:de:0030-drops-235681},
  doi =		{10.4230/LIPIcs.CALCO.2025.9},
  annote =	{Keywords: dynamic logic, many-valued coalgebraic logic, safety, strong completeness}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2025.10
EGGs Are Adhesive!

Authors: Roberto Biondo, Davide Castelnovo, and Fabio Gadducci

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

Abstract
The use of rewriting-based visual formalisms is on the rise. In the formal methods community, this is due also to the introduction of adhesive categories, where most properties of classical approaches to graph transformation, such as those on parallelism and confluence, can be rephrased and proved in a general and uniform way. E-graphs (EGGs) are a formalism for program optimisation via an efficient implementation of equality saturation. In short, EGGs can be defined as (acyclic) term graphs with an additional notion of equivalence on nodes that is closed under the operators of the signature. Instead of replacing the components of a program, the optimisation step is performed by adding new components and linking them to the existing ones via an equivalence relation, until an optimal program is reached. This work describes EGGs via adhesive categories. Besides the benefits in itself of a formal presentation, which renders precise the properties of the data structure, the description of the addition of equivalent program components using standard graph transformation tools offers the advantages of the adhesive framework in modelling, for example, concurrent updates.
Cite as

Roberto Biondo, Davide Castelnovo, and Fabio Gadducci. EGGs Are Adhesive!. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{biondo_et_al:LIPIcs.CALCO.2025.10,
  author =	{Biondo, Roberto and Castelnovo, Davide and Gadducci, Fabio},
  title =	{{EGGs Are Adhesive!}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{10:1--10:18},
  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.2025.10},
  URN =		{urn:nbn:de:0030-drops-235690},
  doi =		{10.4230/LIPIcs.CALCO.2025.10},
  annote =	{Keywords: Hypergraphs, terms graphs, e-graphs, adhesive categories}
}
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
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.2025.29
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
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.2025.30
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.
Cite as

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.CONCUR.2024.11
Left-Linear Rewriting in Adhesive Categories

Authors: Paolo Baldan, Davide Castelnovo, Andrea Corradini, and Fabio Gadducci

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
When can two sequential steps performed by a computing device be considered (causally) independent? This is a relevant question for concurrent and distributed systems, since independence means that they could be executed in any order, and potentially in parallel. Equivalences identifying rewriting sequences which differ only for independent steps are at the core of the theory of concurrency of many formalisms. We investigate the issue in the context of the double pushout approach to rewriting in the general setting of adhesive categories. While a consolidated theory exists for linear rules, which can consume, preserve and generate entities, this paper focuses on left-linear rules which may also "merge" parts of the state. This is an apparently minimal, yet technically hard enhancement, since a standard characterisation of independence that - in the linear case - allows one to derive a number of properties, essential in the development of a theory of concurrency, no longer holds. The paper performs an in-depth study of the notion of independence for left-linear rules: it introduces a novel characterisation of independence, identifies well-behaved classes of left-linear rewriting systems, and provides some fundamental results including a Church-Rosser property and the existence of canonical equivalence proofs for concurrent computations. These results properly extends the class of formalisms that can be modelled in the adhesive framework.
Cite as

Paolo Baldan, Davide Castelnovo, Andrea Corradini, and Fabio Gadducci. Left-Linear Rewriting in Adhesive Categories. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 11:1-11:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{baldan_et_al:LIPIcs.CONCUR.2024.11,
  author =	{Baldan, Paolo and Castelnovo, Davide and Corradini, Andrea and Gadducci, Fabio},
  title =	{{Left-Linear Rewriting in Adhesive Categories}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{11:1--11:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak 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.CONCUR.2024.11},
  URN =		{urn:nbn:de:0030-drops-207835},
  doi =		{10.4230/LIPIcs.CONCUR.2024.11},
  annote =	{Keywords: Adhesive categories, double-pushout rewriting, left-linear rules, switch equivalence, local Church-Rosser property}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.CSL.2024.4
Approximating Fixpoints of Approximated Functions (Invited Talk)

Authors: Barbara König

Published in: LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)

Abstract
There is a large body of work on fixpoint theorems, guaranteeing the existence of fixpoints for certain functions and providing methods for computing them. This includes for instance Banachs’s fixpoint theorem, the well-known result by Knaster-Tarski that is frequently employed in computer science and Kleene iteration. It is less clear how to compute fixpoints if the function whose (least) fixpoint we are interested in is not known exactly, but can only be obtained by a sequence of subsequently better approximations. This scenario occurs for instance in the context of reinforcement learning, where the probabilities of a Markov decision process (MDP) - for which one wants to learn a strategy - are unknown and can only be sampled. There are several solutions to this problem where the fixpoint computation (for determining the value vector and the optimal strategy) and the exploration of the model are interleaved. However, these methods work only well for discounted MDPs, that is in the contractive setting, but not for general MDPs, that is for non-expansive functions. After describing and motivating the problem, we will in particular concentrate on the non-expansive case. There are many interesting systems who value vectors can be obtained by determining the fixpoints of non-expansive functions. Other than contractive functions, they do not guarantee uniqueness of the fixpoint, making it more difficult to approximate the least fixpoint by methods other than Kleene iteration. And also Kleene iteration fails if the function under consideration is only approximated. We hence describe a dampened Mann iteration scheme for (higher-dimensional) functions on the reals that converges to the least fixpoint from everywhere. This scheme can also be adapted to functions that are approximated, under certain conditions. We will in particular study the case of MDPs and consider a related problem that arises when performing model-checking for quantitative mu-calculi, which involves the computation of nested fixpoints. This is joint work with Paolo Baldan, Sebastian Gurke, Tommaso Padoan and Florian Wittbold.
Cite as

Barbara König. Approximating Fixpoints of Approximated Functions (Invited Talk). In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, p. 4:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{konig:LIPIcs.CSL.2024.4,
  author =	{K\"{o}nig, Barbara},
  title =	{{Approximating Fixpoints of Approximated Functions}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{4:1--4:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello 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.CSL.2024.4},
  URN =		{urn:nbn:de:0030-drops-196469},
  doi =		{10.4230/LIPIcs.CSL.2024.4},
  annote =	{Keywords: fixpoints, approximation, Markov decision processes}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.CALCO.2023
LIPIcs, Volume 270, CALCO 2023, Complete Volume

Authors: Paolo Baldan and Valeria de Paiva

Published in: LIPIcs, Volume 270, 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)

Abstract
LIPIcs, Volume 270, CALCO 2023, Complete Volume
Cite as

10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 1-336, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Proceedings{baldan_et_al:LIPIcs.CALCO.2023,
  title =	{{LIPIcs, Volume 270, CALCO 2023, Complete Volume}},
  booktitle =	{10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
  pages =	{1--336},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-287-7},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{270},
  editor =	{Baldan, Paolo and de Paiva, Valeria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2023},
  URN =		{urn:nbn:de:0030-drops-187967},
  doi =		{10.4230/LIPIcs.CALCO.2023},
  annote =	{Keywords: LIPIcs, Volume 270, CALCO 2023, Complete Volume}
}
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