11 Search Results for "Blumensath, Achim"

Document
DOI: 10.4230/DagRep.15.3.177
Categories for Automata and Language Theory (Dagstuhl Seminar 25141)

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

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

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

Achim Blumensath, Mikołaj Bojańczyk, Bartek Klin, and Daniela Petrişan. Categories for Automata and Language Theory (Dagstuhl Seminar 25141). In Dagstuhl Reports, Volume 15, Issue 3, pp. 177-200, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{blumensath_et_al:DagRep.15.3.177,
  author =	{Blumensath, Achim and Boja\'{n}czyk, Miko{\l}aj and Klin, Bartek and Petri\c{s}an, Daniela},
  title =	{{Categories for Automata and Language Theory (Dagstuhl Seminar 25141)}},
  pages =	{177--200},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2025},
  volume =	{15},
  number =	{3},
  editor =	{Blumensath, Achim and Boja\'{n}czyk, Miko{\l}aj and Klin, Bartek and Petri\c{s}an, Daniela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.15.3.177},
  URN =		{urn:nbn:de:0030-drops-248949},
  doi =		{10.4230/DagRep.15.3.177},
  annote =	{Keywords: categorical automata theory, automata theory, category theory, monads}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.51
Word Structures and Their Automatic Presentations

Authors: Xiaoyang Gong, Bakh Khoussainov, and Yuyang Zhuge

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

Abstract
We study automatic presentations of the structures (ℕ; S), (ℕ; E_S), (ℕ; ≤), and their expansions by a unary predicate U. Here S is the successor function, E_S is the undirected version of S, and ≤ is the natural order. We call these structures word structures. Our goal is three-fold. First, we study the isomorphism problem for automatic word structures by focusing on the following three problems. The first problem asks to design an algorithm that, given an automatic structure A, decides if A is isomorphic to (ℕ; S). The second asks to design an algorithm that, given two automatic presentations of (ℕ; S, U₁) and (ℕ; S, U₂), where U₁ and U₂ are unary predicates, decides if these structures are isomorphic. The third problem investigates if there is an algorithm that, given two automatic presentations of (ℕ; ≤, U₁) and (ℕ; ≤, U₂), decides whether U₁ ∩ U₂ ≠ ∅. We show that these problems are undecidable. Next, we study intrinsic regularity of the function S in the structure Path_ω = (ℕ; E_S). We build an automatic presentation of Path_ω in which S is not regular. This implies that S is not intrinsically regular in Path_ω. For U ⊆ ℕ, let d_U be the function that computes the distances between the consecutive elements of U. We build automatic presentations of (ℕ; ≤, U) where d_U can realise logarithmic, radical, intermediate, and exponential functions.
Cite as

Xiaoyang Gong, Bakh Khoussainov, and Yuyang Zhuge. Word Structures and Their Automatic Presentations. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 51:1-51:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gong_et_al:LIPIcs.MFCS.2025.51,
  author =	{Gong, Xiaoyang and Khoussainov, Bakh and Zhuge, Yuyang},
  title =	{{Word Structures and Their Automatic Presentations}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{51:1--51:18},
  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.2025.51},
  URN =		{urn:nbn:de:0030-drops-241581},
  doi =		{10.4230/LIPIcs.MFCS.2025.51},
  annote =	{Keywords: Automatic structures, the isomorphism problem, decidability, undecidability, regular relations}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.31
Games with ω-Automatic Preference Relations

Authors: Véronique Bruyère, Christophe Grandmont, and Jean-François Raskin

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

Abstract
This paper investigates Nash equilibria (NEs) in multi-player turn-based games on graphs, where player preferences are modeled as ω-automatic relations via deterministic parity automata. Unlike much of the existing literature, which focuses on specific reward functions, our results apply to any preference relation definable by an ω-automatic relation. We analyze the computational complexity of determining the existence of an NE (possibly under some constraints), verifying whether a given strategy profile forms an NE, and checking whether a specific outcome can be realized by an NE. When a (constrained) NE exists, we show that there always exists one with finite-memory strategies. Finally, we explore fundamental properties of ω-automatic relations and their implications in the existence of equilibria.
Cite as

Véronique Bruyère, Christophe Grandmont, and Jean-François Raskin. Games with ω-Automatic Preference Relations. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bruyere_et_al:LIPIcs.MFCS.2025.31,
  author =	{Bruy\`{e}re, V\'{e}ronique and Grandmont, Christophe and Raskin, Jean-Fran\c{c}ois},
  title =	{{Games with \omega-Automatic Preference Relations}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{31:1--31:19},
  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.2025.31},
  URN =		{urn:nbn:de:0030-drops-241381},
  doi =		{10.4230/LIPIcs.MFCS.2025.31},
  annote =	{Keywords: Games played on graphs, Nash equilibrium, \omega-automatic relations, \omega-recognizable relations, constrained Nash equilibria existence problem}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.80
On Expansions of Monadic Second-Order Logic with Dynamical Predicates

Authors: Joris Nieuwveld and Joël Ouaknine

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

Abstract
Expansions of the monadic second-order (MSO) theory of the structure ⟨ℕ;<⟩ have been a fertile and active area of research ever since the publication of the seminal papers of Büchi and Elgot & Rabin on the subject in the 1960s. In the present paper, we establish decidability of the MSO theory of ⟨ℕ;<,P⟩, where P ranges over a large class of unary "dynamical" predicates, i.e., sets of non-negative values assumed by certain integer linear recurrence sequences. One of our key technical tools is the novel concept of (effective) prodisjunctivity, which we expect may also find independent applications further afield.
Cite as

Joris Nieuwveld and Joël Ouaknine. On Expansions of Monadic Second-Order Logic with Dynamical Predicates. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 80:1-80:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{nieuwveld_et_al:LIPIcs.MFCS.2025.80,
  author =	{Nieuwveld, Joris and Ouaknine, Jo\"{e}l},
  title =	{{On Expansions of Monadic Second-Order Logic with Dynamical Predicates}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{80:1--80:17},
  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.2025.80},
  URN =		{urn:nbn:de:0030-drops-241879},
  doi =		{10.4230/LIPIcs.MFCS.2025.80},
  annote =	{Keywords: Monadic second-order logic, linear recurrence sequences, decidability, Baker’s theorem}
}
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.2025.142
Online and Feasible Presentability: From Trees to Modal Algebras

Authors: Nikolay Bazhenov, Dariusz Kalociński, and Michał Wrocławski

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

Abstract
We investigate whether every computable member of a given class of structures admits a fully primitive recursive (also known as punctual) or fully P-TIME copy. A class with this property is referred to as punctually robust or P-TIME robust, respectively. We present both positive and negative results for structures corresponding to well-known representations of trees, such as binary trees, ordered trees, sequential (or prefix) trees, and partially ordered (poset) trees. A corollary of one of our results on trees is that semilattices and lattices are not punctually robust. In the main result of the paper, we demonstrate that, unlike Boolean algebras, modal algebras - that is, Boolean algebras with modality - are not punctually robust. The question of whether distributive lattices are punctually robust remains open. The paper contributes to a decades-old program on effective and feasible algebra, which has recently gained momentum due to rapid developments in punctual structure theory and its connections to online presentations of structures.
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Nikolay Bazhenov, Dariusz Kalociński, and Michał Wrocławski. Online and Feasible Presentability: From Trees to Modal Algebras. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 142:1-142:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bazhenov_et_al:LIPIcs.ICALP.2025.142,
  author =	{Bazhenov, Nikolay and Kaloci\'{n}ski, Dariusz and Wroc{\l}awski, Micha{\l}},
  title =	{{Online and Feasible Presentability: From Trees to Modal Algebras}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{142:1--142:20},
  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.2025.142},
  URN =		{urn:nbn:de:0030-drops-235190},
  doi =		{10.4230/LIPIcs.ICALP.2025.142},
  annote =	{Keywords: Algebraic structure, computable structure, fully primitive recursive structure, punctual structure, polynomial-time computable structure, punctual robustness, tree, semilattice, lattice, Boolean algebra, modal algebra}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.152
Tree Algebras and Bisimulation-Invariant MSO on Finite Graphs

Authors: Thomas Colcombet, Amina Doumane, and Denis Kuperberg

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

Abstract
We establish that the bisimulation invariant fragment of MSO over finite transition systems is expressively equivalent over finite transition systems to modal μ-calculus, a question that had remained open for several decades. The proof goes by translating the question to an algebraic framework, and showing that the languages of regular trees that are recognised by finitary tree algebras whose sorts zero and one are finite are the regular ones. This corresponds for trees to a weak form of the key translation of Wilke algebras to omega-semigroup over infinite words, and was also a missing piece in the algebraic theory of regular languages of infinite trees for twenty years.
Cite as

Thomas Colcombet, Amina Doumane, and Denis Kuperberg. Tree Algebras and Bisimulation-Invariant MSO on Finite Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 152:1-152:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{colcombet_et_al:LIPIcs.ICALP.2025.152,
  author =	{Colcombet, Thomas and Doumane, Amina and Kuperberg, Denis},
  title =	{{Tree Algebras and Bisimulation-Invariant MSO on Finite Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{152:1--152:16},
  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.2025.152},
  URN =		{urn:nbn:de:0030-drops-235294},
  doi =		{10.4230/LIPIcs.ICALP.2025.152},
  annote =	{Keywords: MSO, mu-calculus, finite graphs, bisimulation, tree algebra}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.55
Modal Separation of Fixpoint Formulae

Authors: Jean Christoph Jung and Jędrzej Kołodziejski

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

Abstract
Modal separability for modal fixpoint formulae is the problem to decide for two given modal fixpoint formulae φ,φ' whether there is a modal formula ψ that separates them, in the sense that φ ⊧ ψ and ψ ⊧ ¬φ'. We study modal separability and its special case modal definability over various classes of models, such as arbitrary models, finite models, trees, and models of bounded outdegree. Our main results are that modal separability is PSpace-complete over words, that is, models of outdegree ≤ 1, ExpTime-complete over unrestricted and over binary models, and 2-ExpTime-complete over models of outdegree bounded by some d ≥ 3. Interestingly, this latter case behaves fundamentally different from the other cases also in that modal logic does not enjoy the Craig interpolation property over this class. Motivated by this we study also the induced interpolant existence problem as a special case of modal separability, and show that it is coNExpTime-complete and thus harder than validity in the logic. Besides deciding separability, we also investigate the problem of efficient construction of separators. Finally, we consider in a case study the extension of modal fixpoint formulae by graded modalities and investigate separability by modal formulae and graded modal formulae.
Cite as

Jean Christoph Jung and Jędrzej Kołodziejski. Modal Separation of Fixpoint Formulae. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 55:1-55:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jung_et_al:LIPIcs.STACS.2025.55,
  author =	{Jung, Jean Christoph and Ko{\l}odziejski, J\k{e}drzej},
  title =	{{Modal Separation of Fixpoint Formulae}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{55:1--55:20},
  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.2025.55},
  URN =		{urn:nbn:de:0030-drops-228804},
  doi =		{10.4230/LIPIcs.STACS.2025.55},
  annote =	{Keywords: Modal Logic, Fixpoint Logic, Separability, Interpolation}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.19
ω-Forest Algebras and Temporal Logics

Authors: Achim Blumensath and Jakub Lédl

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
We use the algebraic framework for languages of infinite trees introduced in [A. Blumensath, 2020] to derive effective characterisations of various temporal logics, in particular the logic EF (a fragment of CTL) and its counting variant cEF.
Cite as

Achim Blumensath and Jakub Lédl. ω-Forest Algebras and Temporal Logics. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 19:1-19:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{blumensath_et_al:LIPIcs.MFCS.2021.19,
  author =	{Blumensath, Achim and L\'{e}dl, Jakub},
  title =	{{\omega-Forest Algebras and Temporal Logics}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{19:1--19:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.19},
  URN =		{urn:nbn:de:0030-drops-144594},
  doi =		{10.4230/LIPIcs.MFCS.2021.19},
  annote =	{Keywords: forest algebras, temporal logics, bisimulation}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.117
Bisimulation Invariant Monadic-Second Order Logic in the Finite

Authors: Achim Blumensath and Felix Wolf

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We consider bisimulation-invariant monadic second-order logic over various classes of finite transition systems. We present several combinatorial characterisations of when the expressive power of this fragment coincides with that of the modal mu-calculus. Using these characterisations we prove for some simple classes of transition systems that this is indeed the case. In particular, we show that, over the class of all finite transition systems with Cantor-Bendixson rank at most k, bisimulation-invariant MSO coincides with L_mu.
Cite as

Achim Blumensath and Felix Wolf. Bisimulation Invariant Monadic-Second Order Logic in the Finite. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 117:1-117:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{blumensath_et_al:LIPIcs.ICALP.2018.117,
  author =	{Blumensath, Achim and Wolf, Felix},
  title =	{{Bisimulation Invariant Monadic-Second Order Logic in the Finite}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{117:1--117:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.117},
  URN =		{urn:nbn:de:0030-drops-91215},
  doi =		{10.4230/LIPIcs.ICALP.2018.117},
  annote =	{Keywords: bisimulation, monadic second-order logic, composition method}
}
Document
DOI: 10.4230/LIPIcs.STACS.2016.19
On a Fragment of AMSO and Tiling Systems

Authors: Achim Blumensath, Thomas Colcombet, and Pawel Parys

Published in: LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)

Abstract
We prove that satisfiability over infinite words is decidable for a fragment of asymptotic monadic second-order logic. In this fragment we only allow formulae of the form "exists t forall s exists r: phi(r,s,t)", where phi does not use quantifiers over number variables, and variables r and s can be only used simultaneously, in subformulae of the form s < f(x) <= r.
Cite as

Achim Blumensath, Thomas Colcombet, and Pawel Parys. On a Fragment of AMSO and Tiling Systems. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{blumensath_et_al:LIPIcs.STACS.2016.19,
  author =	{Blumensath, Achim and Colcombet, Thomas and Parys, Pawel},
  title =	{{On a Fragment of AMSO and Tiling Systems}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Ollinger, Nicolas and Vollmer, Heribert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.19},
  URN =		{urn:nbn:de:0030-drops-57202},
  doi =		{10.4230/LIPIcs.STACS.2016.19},
  annote =	{Keywords: monadic second-order logic, boundedness, tiling problems}
}
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