7 Search Results for "van Heerdt, Gerco"

Document
DOI: 10.4230/LIPIcs.MFCS.2025.92
On Piecewise Affine Reachability with Bellman Operators

Authors: Anton Varonka and Kazuki Watanabe

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

Abstract
A piecewise affine map is one of the simplest mathematical objects exhibiting complex dynamics. The reachability problem of piecewise affine maps is as follows: Given two vectors s, t ∈ ℚ^d and a piecewise affine map f: ℚ^d → ℚ^d, is there n ∈ ℕ such that fⁿ(s) = t? Koiran, Cosnard, and Garzon show that the reachability problem of piecewise affine maps is undecidable even in dimension 2. Most of the recent progress has been focused on decision procedures for one-dimensional piecewise affine maps, where the reachability problem has been shown to be decidable for some subclasses. However, the general undecidability discouraged research into positive results in arbitrary dimension. In this work, we investigate a rich subclass of piecewise affine maps arising as Bellman operators of Markov decision processes (MDPs). We consider the reachability problem restricted to this subclass and examine its decidability in arbitrary dimensions. We establish that the reachability problem for Bellman operators is decidable in any dimension under either of the following conditions: (i) the target vector t is not the fixed point of the operator f; or (ii) the initial and target vectors s and t are comparable with respect to the componentwise order. Furthermore, we show that the reachability problem for two-dimensional Bellman operators is decidable for arbitrary s, t ∈ ℚ^d, in contrast to the known undecidability of reachability for general piecewise affine maps.
Cite as

Anton Varonka and Kazuki Watanabe. On Piecewise Affine Reachability with Bellman Operators. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 92:1-92:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{varonka_et_al:LIPIcs.MFCS.2025.92,
  author =	{Varonka, Anton and Watanabe, Kazuki},
  title =	{{On Piecewise Affine Reachability with Bellman Operators}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{92:1--92:18},
  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.2025.92},
  URN =		{urn:nbn:de:0030-drops-241998},
  doi =		{10.4230/LIPIcs.MFCS.2025.92},
  annote =	{Keywords: piecewise affine map, reachability, value iteration, Markov decision process, Bellman operator}
}
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
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.CONCUR.2020.44
Residual Nominal Automata

Authors: Joshua Moerman and Matteo Sammartino

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

Abstract
We are motivated by the following question: which nominal languages admit an active learning algorithm? This question was left open in previous work, and is particularly challenging for languages recognised by nondeterministic automata. To answer it, we develop the theory of residual nominal automata, a subclass of nondeterministic nominal automata. We prove that this class has canonical representatives, which can always be constructed via a finite number of observations. This property enables active learning algorithms, and makes up for the fact that residuality - a semantic property - is undecidable for nominal automata. Our construction for canonical residual automata is based on a machine-independent characterisation of residual languages, for which we develop new results in nominal lattice theory. Studying residuality in the context of nominal languages is a step towards a better understanding of learnability of automata with some sort of nondeterminism.
Cite as

Joshua Moerman and Matteo Sammartino. Residual Nominal Automata. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 44:1-44:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{moerman_et_al:LIPIcs.CONCUR.2020.44,
  author =	{Moerman, Joshua and Sammartino, Matteo},
  title =	{{Residual Nominal Automata}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{44:1--44:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.44},
  URN =		{urn:nbn:de:0030-drops-128563},
  doi =		{10.4230/LIPIcs.CONCUR.2020.44},
  annote =	{Keywords: nominal automata, residual automata, derivative language, decidability, closure, exact learning, lattice theory}
}
Document
DOI: 10.4230/LIPIcs.CSL.2020.31
Separation and Renaming in Nominal Sets

Authors: Joshua Moerman and Jurriaan Rot

Published in: LIPIcs, Volume 152, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)

Abstract
Nominal sets provide a foundation for reasoning about names. They are used primarily in syntax with binders, but also, e.g., to model automata over infinite alphabets. In this paper, nominal sets are related to nominal renaming sets, which involve arbitrary substitutions rather than permutations, through a categorical adjunction. In particular, the left adjoint relates the separated product of nominal sets to the Cartesian product of nominal renaming sets. Based on these results, we define the new notion of separated nominal automata. We show that these automata can be exponentially smaller than classical nominal automata, if the semantics is closed under substitutions.
Cite as

Joshua Moerman and Jurriaan Rot. Separation and Renaming in Nominal Sets. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 31:1-31:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{moerman_et_al:LIPIcs.CSL.2020.31,
  author =	{Moerman, Joshua and Rot, Jurriaan},
  title =	{{Separation and Renaming in Nominal Sets}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{31:1--31:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Fern\'{a}ndez, Maribel and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2020.31},
  URN =		{urn:nbn:de:0030-drops-116744},
  doi =		{10.4230/LIPIcs.CSL.2020.31},
  annote =	{Keywords: Nominal sets, Separated product, Adjunction, Automata, Coalgebra}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2019.6
Tree Automata as Algebras: Minimisation and Determinisation

Authors: Gerco van Heerdt, Tobias Kappé, Jurriaan Rot, Matteo Sammartino, and Alexandra Silva

Published in: LIPIcs, Volume 139, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)

Abstract
We study a categorical generalisation of tree automata, as algebras for a fixed endofunctor endowed with initial and final states. Under mild assumptions about the base category, we present a general minimisation algorithm for these automata. We then build upon and extend an existing generalisation of the Nerode equivalence to a categorical setting and relate it to the existence of minimal automata. Finally, we show that generalised types of side-effects, such as non-determinism, can be captured by this categorical framework, leading to a general determinisation procedure.
Cite as

Gerco van Heerdt, Tobias Kappé, Jurriaan Rot, Matteo Sammartino, and Alexandra Silva. Tree Automata as Algebras: Minimisation and Determinisation. In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{vanheerdt_et_al:LIPIcs.CALCO.2019.6,
  author =	{van Heerdt, Gerco and Kapp\'{e}, Tobias and Rot, Jurriaan and Sammartino, Matteo and Silva, Alexandra},
  title =	{{Tree Automata as Algebras: Minimisation and Determinisation}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{6:1--6:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Roggenbach, Markus and Sokolova, Ana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2019.6},
  URN =		{urn:nbn:de:0030-drops-114341},
  doi =		{10.4230/LIPIcs.CALCO.2019.6},
  annote =	{Keywords: tree automata, algebras, minimisation, determinisation, Nerode equivalence}
}
Document
DOI: 10.4230/LIPIcs.CSL.2017.29
CALF: Categorical Automata Learning Framework

Authors: Gerco van Heerdt, Matteo Sammartino, and Alexandra Silva

Published in: LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)

Abstract
Automata learning is a technique that has successfully been applied in verification, with the automaton type varying depending on the application domain. Adaptations of automata learning algorithms for increasingly complex types of automata have to be developed from scratch because there was no abstract theory offering guidelines. This makes it hard to devise such algorithms, and it obscures their correctness proofs. We introduce a simple category-theoretic formalism that provides an appropriately abstract foundation for studying automata learning. Furthermore, our framework establishes formal relations between algorithms for learning, testing, and minimization. We illustrate its generality with two examples: deterministic and weighted automata.
Cite as

Gerco van Heerdt, Matteo Sammartino, and Alexandra Silva. CALF: Categorical Automata Learning Framework. In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, pp. 29:1-29:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{vanheerdt_et_al:LIPIcs.CSL.2017.29,
  author =	{van Heerdt, Gerco and Sammartino, Matteo and Silva, Alexandra},
  title =	{{CALF: Categorical Automata Learning Framework}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  pages =	{29:1--29:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Goranko, Valentin and Dam, Mads},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.29},
  URN =		{urn:nbn:de:0030-drops-76950},
  doi =		{10.4230/LIPIcs.CSL.2017.29},
  annote =	{Keywords: automata learning, category theory}
}
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