18 Search Results for "Wißmann, Thorsten"

Document
DOI: 10.4230/LIPIcs.MFCS.2025.14
Register Automata with Permutations

Authors: Mrudula Balachander, Emmanuel Filiot, Raffaella Gentilini, and Nikos Tzevelekos

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We propose Permutation Deterministic Register Automata (pDRAs), a deterministic register automaton model where we allow permutations of registers in transitions. The model enables minimal canonical representations and pDRAs can be tested for equivalence in polynomial time. The complexity of minimization is between GI (the complexity of graph isomorphism) and NP. We then introduce a subclass of pDRAs, called register automata with fixed permutation policy, where the register permutation discipline is stipulated globally. This class generalizes the model proposed by Benedikt, Ley and Puppis in 2010, and we show that it also admits minimal and canonical representations, based on a finite-index word equivalence relation. As an application, we show that for any regular data language L, the minimal register automaton with fixed permutation policy recognizing L can be actively learned in polynomial time using oracles for membership, equivalence and data-memorability queries. We show that all the oracles can be implemented in polynomial time, and so this yields a polynomial time minimization algorithm.
Cite as

Mrudula Balachander, Emmanuel Filiot, Raffaella Gentilini, and Nikos Tzevelekos. Register Automata with Permutations. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balachander_et_al:LIPIcs.MFCS.2025.14,
  author =	{Balachander, Mrudula and Filiot, Emmanuel and Gentilini, Raffaella and Tzevelekos, Nikos},
  title =	{{Register Automata with Permutations}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{14:1--14:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.14},
  URN =		{urn:nbn:de:0030-drops-241219},
  doi =		{10.4230/LIPIcs.MFCS.2025.14},
  annote =	{Keywords: Register automata, data words, equivalence, minimization, active learning}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.20
Compositional Active Learning of Synchronizing Systems Through Automated Alphabet Refinement

Authors: Léo Henry, Mohammad Reza Mousavi, Thomas Neele, and Matteo Sammartino

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

Abstract
Active automata learning infers automaton models of systems from behavioral observations, a technique successfully applied to a wide range of domains. Compositional approaches for concurrent systems have recently emerged. We take a significant step beyond available results, including those by the authors, and develop a general technique for compositional learning of a synchronizing parallel system with an unknown decomposition. Our approach automatically refines the global alphabet into component alphabets while learning the component models. We develop a theoretical treatment of distributions of alphabets, i.e., sets of possibly overlapping component alphabets. We characterize counter-examples that reveal inconsistencies with global observations, and show how to systematically update the distribution to restore consistency. We present a compositional learning algorithm implementing these ideas, where learning counterexamples precisely correspond to distribution counterexamples under well-defined conditions. We provide an implementation, called CoalA, using the state-of-the-art active learning library LearnLib. Our experiments show that in more than 630 subject systems, CoalA delivers orders of magnitude improvements (up to five orders) in membership queries and in systems with significant concurrency, it also achieves better scalability in the number of equivalence queries.
Cite as

Léo Henry, Mohammad Reza Mousavi, Thomas Neele, and Matteo Sammartino. Compositional Active Learning of Synchronizing Systems Through Automated Alphabet Refinement. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{henry_et_al:LIPIcs.CONCUR.2025.20,
  author =	{Henry, L\'{e}o and Mousavi, Mohammad Reza and Neele, Thomas and Sammartino, Matteo},
  title =	{{Compositional Active Learning of Synchronizing Systems Through Automated Alphabet Refinement}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{20:1--20:22},
  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.2025.20},
  URN =		{urn:nbn:de:0030-drops-239700},
  doi =		{10.4230/LIPIcs.CONCUR.2025.20},
  annote =	{Keywords: Active learning, Compositional methods, Concurrency theory, Labelled transition systems, Formal methods}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.18
A State-Based O(m log n) Partitioning Algorithm for Branching Bisimilarity

Authors: Jan Friso Groote and David N. Jansen

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

Abstract
We present a new O(mlog n) algorithm to calculate branching bisimulation equivalence, which is the finest commonly used behavioural equivalence on labelled transition systems that takes the internal action τ into account. This algorithm combines the simpler data structure of an earlier algorithm for Kripke structures (without action labels) with the memory-efficiency of a later algorithm partitioning sets of labelled transitions. It employs a particularly elegant four-way split of blocks of states, which refines a block under two splitters and isolates all new bottom states, simultaneously. Benchmark results show that this new algorithm outperforms the best known algorithm for branching bisimulation both in time and space.
Cite as

Jan Friso Groote and David N. Jansen. A State-Based O(m log n) Partitioning Algorithm for Branching Bisimilarity. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{groote_et_al:LIPIcs.CONCUR.2025.18,
  author =	{Groote, Jan Friso and Jansen, David N.},
  title =	{{A State-Based O(m log n) Partitioning Algorithm for Branching Bisimilarity}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{18:1--18:16},
  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.2025.18},
  URN =		{urn:nbn:de:0030-drops-239688},
  doi =		{10.4230/LIPIcs.CONCUR.2025.18},
  annote =	{Keywords: Algorithm, Branching bisimulation, Partition refinement of states}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.34
New Fault Domains for Conformance Testing of Finite State Machines

Authors: Frits Vaandrager and Ivo Melse

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

Abstract
A fault domain reflects a tester’s assumptions about faults that may occur in an implementation and that need to be detected during testing. A fault domain that has been widely studied in the literature on black-box conformance testing is the class of finite state machines (FSMs) with at most m states. Numerous strategies for generating test suites have been proposed that guarantee fault coverage for this class. These so-called m-complete test suites grow exponentially in m-n, where n is the number of states of the specification, so one can only run them for small values of m-n. But the assumption that m-n is small is not realistic in practice. In his seminal paper from 1964, Hennie raised the challenge to design checking experiments in which the number of states may increase appreciably. In order to solve this long-standing open problem, we propose (much larger) fault domains that capture the assumption that all states in an implementation can be reached by first performing a sequence from some set A (typically a state cover for the specification), followed by k arbitrary inputs, for some small k. The number of states of FSMs in these fault domains grows exponentially in k. We present a sufficient condition for k-A-completeness of test suites with respect to these fault domains. Our condition implies k-A-completeness of two prominent m-complete test suite generation strategies, the Wp and HSI methods. Thus these strategies are complete for much larger fault domains than those for which they were originally designed, and thereby solve Hennie’s challenge. We show that three other prominent m-complete methods (H, SPY and SPYH) do not always generate k-A-complete test suites.
Cite as

Frits Vaandrager and Ivo Melse. New Fault Domains for Conformance Testing of Finite State Machines. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 34:1-34:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vaandrager_et_al:LIPIcs.CONCUR.2025.34,
  author =	{Vaandrager, Frits and Melse, Ivo},
  title =	{{New Fault Domains for Conformance Testing of Finite State Machines}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{34:1--34:22},
  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.2025.34},
  URN =		{urn:nbn:de:0030-drops-239843},
  doi =		{10.4230/LIPIcs.CONCUR.2025.34},
  annote =	{Keywords: conformance testing, finite state machines, Mealy machines, apartness, observation tree, fault domains, k-A-complete test suites}
}
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
(Co)algebraic pearl
DOI: 10.4230/LIPIcs.CALCO.2025.15
Trees in Coalgebra from Generalized Reachability ((Co)algebraic pearl)

Authors: Thorsten Wißmann, Bálint Kocsis, Jurriaan Rot, and Ruben Turkenburg

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

Abstract
An automaton is called reachable if every state is reachable from the initial state. This notion has been generalized coalgebraically in two ways: first, via a universal property on pointed coalgebras, namely, that a reachable coalgebra has no proper subcoalgebra; and second, a coalgebra is reachable if it arises as the union of an iterative computation of successor states, starting from the initial state. In the current paper, we present corresponding universal properties and iterative constructions for trees. The universal property captures when a coalgebra is a tree, namely, when it has no proper tree unravelling. The iterative construction unravels an arbitrary coalgebra to a tree. We show that this yields the expected notion of tree for a variety of standard examples. We obtain our characterization of trees by first generalizing the previous theory of reachable coalgebras. Surprisingly, both the universal property and the iterative construction for trees arise as an instance of this generalized notion of reachability.
Cite as

Thorsten Wißmann, Bálint Kocsis, Jurriaan Rot, and Ruben Turkenburg. Trees in Coalgebra from Generalized Reachability ((Co)algebraic pearl). In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{wimann_et_al:LIPIcs.CALCO.2025.15,
  author =	{Wi{\ss}mann, Thorsten and Kocsis, B\'{a}lint and Rot, Jurriaan and Turkenburg, Ruben},
  title =	{{Trees in Coalgebra from Generalized Reachability}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{15:1--15:18},
  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.2025.15},
  URN =		{urn:nbn:de:0030-drops-235740},
  doi =		{10.4230/LIPIcs.CALCO.2025.15},
  annote =	{Keywords: Trees, Coalgebra, Factorization Systems}
}
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
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.172
Weighted GKAT: Completeness and Complexity

Authors: Spencer Van Koevering, Wojciech Różowski, and Alexandra Silva

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

Abstract
We propose Weighted Guarded Kleene Algebra with Tests (wGKAT), an uninterpreted weighted programming language equipped with branching, conditionals, and loops. We provide an operational semantics for wGKAT using a variant of weighted automata and introduce a sound and complete axiomatization. We also provide a polynomial time decision procedure for bisimulation equivalence.
Cite as

Spencer Van Koevering, Wojciech Różowski, and Alexandra Silva. Weighted GKAT: Completeness and Complexity. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 172:1-172:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vankoevering_et_al:LIPIcs.ICALP.2025.172,
  author =	{Van Koevering, Spencer and R\'{o}\.{z}owski, Wojciech and Silva, Alexandra},
  title =	{{Weighted GKAT: Completeness and Complexity}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{172:1--172:18},
  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.2025.172},
  URN =		{urn:nbn:de:0030-drops-235492},
  doi =		{10.4230/LIPIcs.ICALP.2025.172},
  annote =	{Keywords: Weighted Programming, Automata, Axiomatization, Decision Procedure}
}
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.2025.29
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.CALCO.2023.12
Bisimilar States in Uncertain Structures

Authors: Jurriaan Rot and Thorsten Wißmann

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

Abstract
We provide a categorical notion called uncertain bisimilarity, which allows to reason about bisimilarity in combination with a lack of knowledge about the involved systems. Such uncertainty arises naturally in automata learning algorithms, where one investigates whether two observed behaviours come from the same internal state of a black-box system that can not be transparently inspected. We model this uncertainty as a set functor equipped with a partial order which describes possible future developments of the learning game. On such a functor, we provide a lifting-based definition of uncertain bisimilarity and verify basic properties. Beside its applications to Mealy machines, a natural model for automata learning, our framework also instantiates to an existing compatibility relation on suspension automata, which are used in model-based testing. We show that uncertain bisimilarity is a necessary but not sufficient condition for two states being implementable by the same state in the black-box system. We remedy the lack of sufficiency by a characterization of uncertain bisimilarity in terms of coalgebraic simulations.
Cite as

Jurriaan Rot and Thorsten Wißmann. Bisimilar States in Uncertain Structures. In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{rot_et_al:LIPIcs.CALCO.2023.12,
  author =	{Rot, Jurriaan and Wi{\ss}mann, Thorsten},
  title =	{{Bisimilar States in Uncertain Structures}},
  booktitle =	{10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
  pages =	{12:1--12:17},
  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.2023.12},
  URN =		{urn:nbn:de:0030-drops-188094},
  doi =		{10.4230/LIPIcs.CALCO.2023.12},
  annote =	{Keywords: Coalgebra, Relation Lifting, Bisimilarity, Mealy Machines, ioco}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2023.137
Action Codes

Authors: Frits Vaandrager and Thorsten Wißmann

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
We provide a new perspective on the problem how high-level state machine models with abstract actions can be related to low-level models in which these actions are refined by sequences of concrete actions. We describe the connection between high-level and low-level actions using action codes, a variation of the prefix codes known from coding theory. For each action code ℛ, we introduce a contraction operator α_ℛ that turns a low-level model ℳ into a high-level model, and a refinement operator ϱ_ℛ that transforms a high-level model 𝒩 into a low-level model. We establish a Galois connection ϱ_ℛ(𝒩) ⊑ ℳ ⇔ 𝒩 ⊑ α_ℛ(ℳ), where ⊑ is the well-known simulation preorder. For conformance, we typically want to obtain an overapproximation of model ℳ. To this end, we also introduce a concretization operator γ_ℛ, which behaves like the refinement operator but adds arbitrary behavior at intermediate points, giving us a second Galois connection α_ℛ(ℳ) ⊑ 𝒩 ⇔ ℳ ⊑ γ_ℛ(𝒩). Action codes may be used to construct adaptors that translate between concrete and abstract actions during learning and testing of Mealy machines. If Mealy machine ℳ models a black-box system then α_ℛ(ℳ) describes the behavior that can be observed by a learner/tester that interacts with this system via an adaptor derived from code ℛ. Whenever α_ℛ(ℳ) implements (or conforms to) 𝒩, we may conclude that ℳ implements (or conforms to) γ_ℛ (𝒩). Almost all results, examples, and counter-examples are formalized in Coq.
Cite as

Frits Vaandrager and Thorsten Wißmann. Action Codes. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 137:1-137:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{vaandrager_et_al:LIPIcs.ICALP.2023.137,
  author =	{Vaandrager, Frits and Wi{\ss}mann, Thorsten},
  title =	{{Action Codes}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{137:1--137:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel 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.2023.137},
  URN =		{urn:nbn:de:0030-drops-181895},
  doi =		{10.4230/LIPIcs.ICALP.2023.137},
  annote =	{Keywords: Automata, Models of Reactive Systems, LTS, Action Codes, Action Refinement, Action Contraction, Galois Connection, Model-Based Testing, Model Learning}
}
Document
DOI: 10.4230/LIPIcs.CSL.2023.38
Supported Sets - A New Foundation for Nominal Sets and Automata

Authors: Thorsten Wißmann

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)

Abstract
The present work proposes and discusses the category of supported sets which provides a uniform foundation for nominal sets of various kinds, such as those for equality symmetry, for the order symmetry, and renaming sets. We show that all these differently flavoured categories of nominal sets are monadic over supported sets. Thus, supported sets provide a canonical finite way to represent nominal sets and the automata therein, e.g. register automata and coalgebras in general. Name binding in supported sets is modelled by a functor following the idea of de Bruijn indices. This functor lifts to the well-known abstraction functor in nominal sets. Together with the monadicity result, this gives rise to a transformation process from finite coalgebras in supported sets to orbit-finite coalgebras in nominal sets. One instance of this process transforms the finite representation of a register automaton in supported sets into its configuration automaton in nominal sets.
Cite as

Thorsten Wißmann. Supported Sets - A New Foundation for Nominal Sets and Automata. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 38:1-38:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{wimann:LIPIcs.CSL.2023.38,
  author =	{Wi{\ss}mann, Thorsten},
  title =	{{Supported Sets - A New Foundation for Nominal Sets and Automata}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{38:1--38:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.38},
  URN =		{urn:nbn:de:0030-drops-174992},
  doi =		{10.4230/LIPIcs.CSL.2023.38},
  annote =	{Keywords: Nominal Sets, Monads, LFP-Category, Supported Sets, Coalgebra}
}
Document
(Co)algebraic pearls
DOI: 10.4230/LIPIcs.CALCO.2021.24
Minimality Notions via Factorization Systems ((Co)algebraic pearls)

Authors: Thorsten Wißmann

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

Abstract
For the minimization of state-based systems (i.e. the reduction of the number of states while retaining the system’s semantics), there are two obvious aspects: removing unnecessary states of the system and merging redundant states in the system. In the present article, we relate the two aspects on coalgebras by defining an abstract notion of minimality. The abstract notion minimality and minimization live in a general category with a factorization system. We will find criteria on the category that ensure uniqueness, existence, and functoriality of the minimization aspects. The proofs of these results instantiate to those for reachability and observability minimization in the standard coalgebra literature. Finally, we will see how the two aspects of minimization interact and under which criteria they can be sequenced in any order, like in automata minimization.
Cite as

Thorsten Wißmann. Minimality Notions via Factorization Systems ((Co)algebraic pearls). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 24:1-24:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{wimann:LIPIcs.CALCO.2021.24,
  author =	{Wi{\ss}mann, Thorsten},
  title =	{{Minimality Notions via Factorization Systems}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{24:1--24:21},
  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.2021.24},
  URN =		{urn:nbn:de:0030-drops-153791},
  doi =		{10.4230/LIPIcs.CALCO.2021.24},
  annote =	{Keywords: Coalgebra, Reachability, Observability, Minimization, Factorization System}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2021.32
Explaining Behavioural Inequivalence Generically in Quasilinear Time

Authors: Thorsten Wißmann, Stefan Milius, and Lutz Schröder

Published in: LIPIcs, Volume 203, 32nd International Conference on Concurrency Theory (CONCUR 2021)

Abstract
We provide a generic algorithm for constructing formulae that distinguish behaviourally inequivalent states in systems of various transition types such as nondeterministic, probabilistic or weighted; genericity over the transition type is achieved by working with coalgebras for a set functor in the paradigm of universal coalgebra. For every behavioural equivalence class in a given system, we construct a formula which holds precisely at the states in that class. The algorithm instantiates to deterministic finite automata, transition systems, labelled Markov chains, and systems of many other types. The ambient logic is a modal logic featuring modalities that are generically extracted from the functor; these modalities can be systematically translated into custom sets of modalities in a postprocessing step. The new algorithm builds on an existing coalgebraic partition refinement algorithm. It runs in time 𝒪((m+n) log n) on systems with n states and m transitions, and the same asymptotic bound applies to the dag size of the formulae it constructs. This improves the bounds on run time and formula size compared to previous algorithms even for previously known specific instances, viz. transition systems and Markov chains; in particular, the best previous bound for transition systems was 𝒪(m n).
Cite as

Thorsten Wißmann, Stefan Milius, and Lutz Schröder. Explaining Behavioural Inequivalence Generically in Quasilinear Time. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 32:1-32:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{wimann_et_al:LIPIcs.CONCUR.2021.32,
  author =	{Wi{\ss}mann, Thorsten and Milius, Stefan and Schr\"{o}der, Lutz},
  title =	{{Explaining Behavioural Inequivalence Generically in Quasilinear Time}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{32:1--32:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2021.32},
  URN =		{urn:nbn:de:0030-drops-144094},
  doi =		{10.4230/LIPIcs.CONCUR.2021.32},
  annote =	{Keywords: bisimulation, partition refinement, modal logic, distinguishing formulae, coalgebra}
}
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