6 Search Results for "Keskin, Eren"

Document
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2025.2
Unboundedness Problems for Formal Languages (Invited Talk)

Authors: Georg Zetzsche

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
Informally, unboundedness problems are decision problems that ask about the existence of infinitely many words (satisfying certain properties) in a formal language. For example: Is a given language infinite? Or: Does a given language have super-polynomial growth? These came into focus in recent years because of their connections to downward closure computation and separability problems. Although unboundedness problems may seem difficult at first, it turns out that there are techniques that are at the same time conceptually very simple, but also apply to a surprisingly wide variety of language classes. The talk will survey recent results (and techniques) concerning unboundedness problems.
Cite as

Georg Zetzsche. Unboundedness Problems for Formal Languages (Invited Talk). In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 2:1-2:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zetzsche:LIPIcs.FSTTCS.2025.2,
  author =	{Zetzsche, Georg},
  title =	{{Unboundedness Problems for Formal Languages}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{2:1--2:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.2},
  URN =		{urn:nbn:de:0030-drops-250810},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.2},
  annote =	{Keywords: Decidability, formal languages, unifying frameworks, downward closure, separability}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.38
The Complexity of Separability for Semilinear Sets and Parikh Automata

Authors: Elias Rojas Collins, Chris Köcher, and Georg Zetzsche

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

Abstract
In a separability problem, we are given two sets K and L from a class 𝒞, and we want to decide whether there exists a set S from a class 𝒮 such that K ⊆ S and S ∩ L = ∅. In this case, we speak of separability of sets in 𝒞 by sets in 𝒮. We study two types of separability problems. First, we consider separability of semilinear sets (i.e. subsets of ℕ^d for some d) by sets definable by quantifier-free monadic Presburger formulas (or equivalently, the recognizable subsets of ℕ^d). Here, a formula is monadic if each atom uses at most one variable. Second, we consider separability of languages of Parikh automata by regular languages. A Parikh automaton is a machine with access to counters that can only be incremented, and have to meet a semilinear constraint at the end of the run. Both of these separability problems are known to be decidable with elementary complexity. Our main results are that both problems are coNP-complete. In the case of semilinear sets, coNP-completeness holds regardless of whether the input sets are specified by existential Presburger formulas, quantifier-free formulas, or semilinear representations. Our results imply that recognizable separability of rational subsets of Σ* × ℕ^d (shown decidable by Choffrut and Grigorieff) is coNP-complete as well. Another application is that regularity of deterministic Parikh automata (where the target set is specified using a quantifier-free Presburger formula) is coNP-complete as well.
Cite as

Elias Rojas Collins, Chris Köcher, and Georg Zetzsche. The Complexity of Separability for Semilinear Sets and Parikh Automata. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 38:1-38:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{collins_et_al:LIPIcs.MFCS.2025.38,
  author =	{Collins, Elias Rojas and K\"{o}cher, Chris and Zetzsche, Georg},
  title =	{{The Complexity of Separability for Semilinear Sets and Parikh Automata}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{38:1--38:21},
  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.2025.38},
  URN =		{urn:nbn:de:0030-drops-241457},
  doi =		{10.4230/LIPIcs.MFCS.2025.38},
  annote =	{Keywords: Vector Addition System, Separability, Regular Language}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.13
Languages of Boundedly-Ambiguous Vector Addition Systems with States

Authors: Wojciech Czerwiński and Łukasz Orlikowski

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

Abstract
The aim of this paper is to deliver broad understanding of a class of languages of boundedly-ambiguous VASSs, that is k-ambiguous VASSs for some natural k. These are languages of Vector Addition Systems with States with the acceptance condition defined by the set of accepting states such that each accepted word has at most k accepting runs. We develop tools for proving that a given language is not accepted by any k-ambiguous VASS. Using them we show a few negative results: lack of some closure properties of languages of k-ambiguous VASSs and undecidability of the k-ambiguity problem, namely the question whether a given VASS language is a language of some k-ambiguous VASS. In fact we show an even more general undecidability result stating that for any class containing all regular languages and only k-ambiguous VASS languages for some k ∈ ℕ it is undecidable whether a language of a given 1-dimensional VASS belongs to this class. Finally, we show that the regularity problem is decidable for k-ambiguous VASSs.
Cite as

Wojciech Czerwiński and Łukasz Orlikowski. Languages of Boundedly-Ambiguous Vector Addition Systems with States. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 13:1-13:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{czerwinski_et_al:LIPIcs.CONCUR.2025.13,
  author =	{Czerwi\'{n}ski, Wojciech and Orlikowski, {\L}ukasz},
  title =	{{Languages of Boundedly-Ambiguous Vector Addition Systems with States}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{13:1--13:23},
  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.2025.13},
  URN =		{urn:nbn:de:0030-drops-239635},
  doi =		{10.4230/LIPIcs.CONCUR.2025.13},
  annote =	{Keywords: vector addition systems, Petri nets, unambiguity, bounded-ambiguity, languages}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.126
Separability in Büchi VASS and Singly Non-Linear Systems of Inequalities

Authors: Pascal Baumann, Eren Keskin, Roland Meyer, and Georg Zetzsche

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
The ω-regular separability problem for Büchi VASS coverability languages has recently been shown to be decidable, but with an EXPSPACE lower and a non-primitive recursive upper bound - the exact complexity remained open. We close this gap and show that the problem is EXPSPACE-complete. A careful analysis of our complexity bounds additionally yields a PSPACE procedure in the case of fixed dimension ≥ 1, which matches a pre-established lower bound of PSPACE for one dimensional Büchi VASS. Our algorithm is a non-deterministic search for a witness whose size, as we show, can be suitably bounded. Part of the procedure is to decide the existence of runs in VASS that satisfy certain non-linear properties. Therefore, a key technical ingredient is to analyze a class of systems of inequalities where one variable may occur in non-linear (polynomial) expressions. These so-called singly non-linear systems (SNLS) take the form A(x)⋅ y ≥ b(x), where A(x) and b(x) are a matrix resp. a vector whose entries are polynomials in x, and y ranges over vectors in the rationals. Our main contribution on SNLS is an exponential upper bound on the size of rational solutions to singly non-linear systems. The proof consists of three steps. First, we give a tailor-made quantifier elimination to characterize all real solutions to x. Second, using the root separation theorem about the distance of real roots of polynomials, we show that if a rational solution exists, then there is one with at most polynomially many bits. Third, we insert the solution for x into the SNLS, making it linear and allowing us to invoke standard solution bounds from convex geometry. Finally, we combine the results about SNLS with several techniques from the area of VASS to devise an EXPSPACE decision procedure for ω-regular separability of Büchi VASS.
Cite as

Pascal Baumann, Eren Keskin, Roland Meyer, and Georg Zetzsche. Separability in Büchi VASS and Singly Non-Linear Systems of Inequalities. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 126:1-126:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{baumann_et_al:LIPIcs.ICALP.2024.126,
  author =	{Baumann, Pascal and Keskin, Eren and Meyer, Roland and Zetzsche, Georg},
  title =	{{Separability in B\"{u}chi VASS and Singly Non-Linear Systems of Inequalities}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{126:1--126:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.126},
  URN =		{urn:nbn:de:0030-drops-202695},
  doi =		{10.4230/LIPIcs.ICALP.2024.126},
  annote =	{Keywords: Vector addition systems, infinite words, separability, inequalities, quantifier elimination, rational, polynomials}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.142
An Efficient Quantifier Elimination Procedure for Presburger Arithmetic

Authors: Christoph Haase, Shankara Narayanan Krishna, Khushraj Madnani, Om Swostik Mishra, and Georg Zetzsche

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
All known quantifier elimination procedures for Presburger arithmetic require doubly exponential time for eliminating a single block of existentially quantified variables. It has even been claimed in the literature that this upper bound is tight. We observe that this claim is incorrect and develop, as the main result of this paper, a quantifier elimination procedure eliminating a block of existentially quantified variables in singly exponential time. As corollaries, we can establish the precise complexity of numerous problems. Examples include deciding (i) monadic decomposability for existential formulas, (ii) whether an existential formula defines a well-quasi ordering or, more generally, (iii) certain formulas of Presburger arithmetic with Ramsey quantifiers. Moreover, despite the exponential blowup, our procedure shows that under mild assumptions, even NP upper bounds for decision problems about quantifier-free formulas can be transferred to existential formulas. The technical basis of our results is a kind of small model property for parametric integer programming that generalizes the seminal results by von zur Gathen and Sieveking on small integer points in convex polytopes.
Cite as

Christoph Haase, Shankara Narayanan Krishna, Khushraj Madnani, Om Swostik Mishra, and Georg Zetzsche. An Efficient Quantifier Elimination Procedure for Presburger Arithmetic. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 142:1-142:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{haase_et_al:LIPIcs.ICALP.2024.142,
  author =	{Haase, Christoph and Krishna, Shankara Narayanan and Madnani, Khushraj and Mishra, Om Swostik and Zetzsche, Georg},
  title =	{{An Efficient Quantifier Elimination Procedure for Presburger Arithmetic}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{142:1--142:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.142},
  URN =		{urn:nbn:de:0030-drops-202856},
  doi =		{10.4230/LIPIcs.ICALP.2024.142},
  annote =	{Keywords: Presburger arithmetic, quantifier elimination, parametric integer programming, convex geometry}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2023.8
Separability and Non-Determinizability of WSTS

Authors: Eren Keskin and Roland Meyer

Published in: LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

Abstract
There is a recent separability result for the languages of well-structured transition systems (WSTS) that is surprisingly general: disjoint WSTS languages are always separated by a regular language. The result assumes that one of the languages is accepted by a deterministic WSTS, and it is not known whether this assumption is needed. There are two ways to get rid of the assumption, none of which has led to conclusions so far: (i) show that WSTS can be determinized or (ii) generalize the separability result to non-deterministic WSTS languages. Our contribution is to show that (i) does not work but (ii) does. As for (i), we give a non-deterministic WSTS language that we prove cannot be accepted by a deterministic WSTS. The proof relies on a novel characterization of the languages accepted by deterministic WSTS. As for (ii), we show how to find finitely represented inductive invariants without having the tool of ideal decompositions at hand. Instead, we work with closures under converging sequences. Our results hold for upward- and downward-compatible WSTS.
Cite as

Eren Keskin and Roland Meyer. Separability and Non-Determinizability of WSTS. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{keskin_et_al:LIPIcs.CONCUR.2023.8,
  author =	{Keskin, Eren and Meyer, Roland},
  title =	{{Separability and Non-Determinizability of WSTS}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{8:1--8:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-299-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{279},
  editor =	{P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.8},
  URN =		{urn:nbn:de:0030-drops-190025},
  doi =		{10.4230/LIPIcs.CONCUR.2023.8},
  annote =	{Keywords: WSTS, regular separability, determinization}
}
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