LIPIcs, Volume 272

48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)



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Event

MFCS 2023, August 28 to September 1, 2023, Bordeaux, France

Editors

Jérôme Leroux
  • LaBRI, Université Bordeaux, CNRS, Bordeaux-INP, Talence, France
Sylvain Lombardy
  • LaBRI, Université Bordeaux, CNRS, Bordeaux-INP, Talence, France
David Peleg
  • Weizmann Institute of Science, Rehovot, Israel

Publication Details

  • published at: 2023-08-21
  • Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
  • ISBN: 978-3-95977-292-1
  • DBLP: db/conf/mfcs/mfcs2023

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Document
Complete Volume
LIPIcs, Volume 272, MFCS 2023, Complete Volume

Authors: Jérôme Leroux, Sylvain Lombardy, and David Peleg


Abstract
LIPIcs, Volume 272, MFCS 2023, Complete Volume

Cite as

48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 1-1302, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@Proceedings{leroux_et_al:LIPIcs.MFCS.2023,
  title =	{{LIPIcs, Volume 272, MFCS 2023, Complete Volume}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{1--1302},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023},
  URN =		{urn:nbn:de:0030-drops-185332},
  doi =		{10.4230/LIPIcs.MFCS.2023},
  annote =	{Keywords: LIPIcs, Volume 272, MFCS 2023, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Jérôme Leroux, Sylvain Lombardy, and David Peleg


Abstract
Front Matter, Table of Contents, Preface, Conference Organization

Cite as

48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{leroux_et_al:LIPIcs.MFCS.2023.0,
  author =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{0:i--0:xviii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.0},
  URN =		{urn:nbn:de:0030-drops-185349},
  doi =		{10.4230/LIPIcs.MFCS.2023.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
Exploring the Space of Colourings with Kempe Changes (Invited Talk)

Authors: Marthe Bonamy


Abstract
Kempe changes were introduced in 1879 in an attempt to prove the 4-colour theorem. They are a convenient if not crucial tool to prove various colouring theorems. Here, we consider how to navigate from a colouring to another through Kempe changes. When is it possible? How fast?

Cite as

Marthe Bonamy. Exploring the Space of Colourings with Kempe Changes (Invited Talk). In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 1:1-1:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bonamy:LIPIcs.MFCS.2023.1,
  author =	{Bonamy, Marthe},
  title =	{{Exploring the Space of Colourings with Kempe Changes}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{1:1--1:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.1},
  URN =		{urn:nbn:de:0030-drops-185350},
  doi =		{10.4230/LIPIcs.MFCS.2023.1},
  annote =	{Keywords: Graph theory, graph coloring, reconfiguration}
}
Document
Invited Talk
Online Algorithms with Predictions (Invited Talk)

Authors: Joan Boyar


Abstract
We give an introduction to online algorithms with predictions, from an algorithms researcher’s perspective, concentrating on minimization problems.

Cite as

Joan Boyar. Online Algorithms with Predictions (Invited Talk). In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 2:1-2:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{boyar:LIPIcs.MFCS.2023.2,
  author =	{Boyar, Joan},
  title =	{{Online Algorithms with Predictions}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{2:1--2:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.2},
  URN =		{urn:nbn:de:0030-drops-185368},
  doi =		{10.4230/LIPIcs.MFCS.2023.2},
  annote =	{Keywords: Online algorithms with predictions, online algorithms with advice, random order analysis}
}
Document
Invited Talk
Modern Parallel Algorithms (Invited Talk)

Authors: Artur Czumaj


Abstract
Recent advances in the design of efficient parallel algorithms have been largely focusing on the nowadays classical model of parallel computing called Massive Parallel Computation (MPC), which follows the framework of MapReduce systems. In this talk we will survey recent advances in the design of algorithms for graph problems for the MPC model and will mention some interesting open questions in this area.

Cite as

Artur Czumaj. Modern Parallel Algorithms (Invited Talk). In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 3:1-3:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{czumaj:LIPIcs.MFCS.2023.3,
  author =	{Czumaj, Artur},
  title =	{{Modern Parallel Algorithms}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{3:1--3:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.3},
  URN =		{urn:nbn:de:0030-drops-185378},
  doi =		{10.4230/LIPIcs.MFCS.2023.3},
  annote =	{Keywords: Distributed computing, parallel computing}
}
Document
Invited Talk
Algebraic Reasoning for (Un)Solvable Loops (Invited Talk)

Authors: Laura Kovács


Abstract
Loop invariants describe valid program properties that hold before and after every loop iteration. As such, loop invariants are the workhorses in formalizing loop semantics and automating the formal analysis and verification of programs with loops. While automatically synthesizing loop invariants is, in general, an uncomputable problem, when considering only single-path loops with linear updates (linear loops), the strongest polynomial invariant is in fact computable [Michael Karr, 1976; Markus Müller-Olm and Helmut Seidl, 2004; Laura Kovács, 2008; Ehud Hrushovski et al., 2018]. Yet, already for loops with "only" polynomial updates, computing the strongest invariant has been an open challenge since 2004 [Markus Müller-Olm and Helmut Seidl, 2004]. In this invited talk, we first present computability results on polynomial invariant synthesis for restricted polynomial loops, called solvable loops [Rodríguez-Carbonell and Kapur, 2004]. Key to solvable loops is that one can automatically compute invariants from closed-form solutions of algebraic recurrence equations that model the loop behaviour [Laura Kovács, 2008; Andreas Humenberger et al., 2017]. We also establish a technique for invariant synthesis for classes of loops that are not solvable, termed unsolvable loops [Daneshvar Amrollahi et al., 2022]. We next study the limits of computability in deriving the (strongest) polynomial invariants for arbitrary polynomial loops. We prove that computing the strongest polynomial invariant of arbitrary, single-path polynomial loops is very hard [Julian Müllner, 2023] - namely, it is at least as hard as the Skolem problem [Graham Everest et al., 2003; Terrence Tao, 2008], a prominent algebraic problem in the theory of linear recurrences. Going beyond single-path loops, we show that the strongest polynomial invariant is uncomputable already for multi-path polynomial loops with arbitrary quadratic polynomial updates [Laura Kovács and Anton Varonka, 2023].

Cite as

Laura Kovács. Algebraic Reasoning for (Un)Solvable Loops (Invited Talk). In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 4:1-4:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{kovacs:LIPIcs.MFCS.2023.4,
  author =	{Kov\'{a}cs, Laura},
  title =	{{Algebraic Reasoning for (Un)Solvable Loops}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{4:1--4:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.4},
  URN =		{urn:nbn:de:0030-drops-185385},
  doi =		{10.4230/LIPIcs.MFCS.2023.4},
  annote =	{Keywords: Symbolic Computation, Formal Methods, Loop Analysis, Polynomial Invariants}
}
Document
Invited Talk
Sliding into the Future: Investigating Sliding Windows in Temporal Graphs (Invited Talk)

Authors: Nina Klobas, George B. Mertzios, and Paul G. Spirakis


Abstract
Graphs are fundamental tools for modelling relations among objects in various scientific fields. However, traditional static graphs have limitations when it comes to capturing the dynamic nature of real-world systems. To overcome this limitation, temporal graphs have been introduced as a framework to model graphs that change over time. In temporal graphs the edges among vertices appear and disappear at specific time steps, reflecting the temporal dynamics of the observed system, which allows us to analyse time dependent patterns and processes. In this paper we focus on the research related to sliding time windows in temporal graphs. Sliding time windows offer a way to analyse specific time intervals within the lifespan of a temporal graph. By sliding the window along the timeline, we can examine the graph’s characteristics and properties within different time periods. This paper provides an overview of the research on sliding time windows in temporal graphs. Although progress has been made in this field, there are still many interesting questions and challenges to be explored. We discuss some of the open problems and highlight their potential for future research.

Cite as

Nina Klobas, George B. Mertzios, and Paul G. Spirakis. Sliding into the Future: Investigating Sliding Windows in Temporal Graphs (Invited Talk). In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 5:1-5:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{klobas_et_al:LIPIcs.MFCS.2023.5,
  author =	{Klobas, Nina and Mertzios, George B. and Spirakis, Paul G.},
  title =	{{Sliding into the Future: Investigating Sliding Windows in Temporal Graphs}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{5:1--5:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.5},
  URN =		{urn:nbn:de:0030-drops-185397},
  doi =		{10.4230/LIPIcs.MFCS.2023.5},
  annote =	{Keywords: Temporal Graphs, Sliding Time Windows}
}
Document
Roman Census: Enumerating and Counting Roman Dominating Functions on Graph Classes

Authors: Faisal N. Abu-Khzam, Henning Fernau, and Kevin Mann


Abstract
The concept of Roman domination has recently been studied concerning enumerating and counting in F. N. Abu-Khzam et al. (WG 2022). More technically speaking, a function that assigns 0,1,2 to the vertices of an undirected graph is called a Roman dominating function if each vertex assigned zero has a neighbor assigned two. Such a function is called minimal if decreasing any assignment to any vertex would yield a function that is no longer a Roman dominating function. It has been shown that minimal Roman dominating functions can be enumerated with polynomial delay, i.e., between any two outputs of a solution, no more than polynomial time will elapse. This contrasts what is known about minimal dominating sets, where the question whether or not these can be enumerated with polynomial delay is open for more than 40 years. This makes the concept of Roman domination rather special and interesting among the many variants of domination problems studied in the literature, as it has been shown for several of these variants that the question of enumerating minimal solutions is tightly linked to that of enumerating minimal dominating sets, see M. Kanté et al. in SIAM J. Disc. Math., 2014. The running time of the mentioned enumeration algorithm for minimal Roman dominating functions (Abu-Khzam et al., WG 2022) could be estimated as 𝒪(1.9332ⁿ) on general graphs of order n. Here, we focus on special graph classes, as has been also done for enumerating minimal dominating sets before. More specifically, for chordal graphs, we present an enumeration algorithm running in time 𝒪(1.8940ⁿ). It is unknown if this gives a tight bound on the maximum number of minimal Roman dominating functions in chordal graphs. For interval graphs, we can lower this time bound further to 𝒪(1.7321ⁿ), which also matches the known lower bound concerning the maximum number of minimal Roman dominating functions. We can also provide a matching lower and upper bound for forests, which is (incidentally) the same, namely 𝒪^*(√3ⁿ). Furthermore, we present an optimal enumeration algorithm running in time 𝒪^*(∛3ⁿ) for split graphs and for cobipartite graphs, i.e., we can also give a matching lower bound example for these graph classes. Hence, our enumeration algorithms for interval graphs, forests, split graphs and cobipartite graphs are all optimal. The importance of our results stems from the fact that, for other types of domination problems, optimal enumeration algorithms are not always found. Interestingly, we use a different form of analysis for the running times of our different algorithms, and the branchings had to be tailored and tweaked to obtain the intended optimality results. Our Roman dominating functions enumeration algorithm for trees and forests is distinctively different from the one for minimal dominating sets by Rote (SODA 2019).Our approach also allows to give concrete formulas for counting minimal Roman dominating functions on more concrete graph families like paths.

Cite as

Faisal N. Abu-Khzam, Henning Fernau, and Kevin Mann. Roman Census: Enumerating and Counting Roman Dominating Functions on Graph Classes. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{abukhzam_et_al:LIPIcs.MFCS.2023.6,
  author =	{Abu-Khzam, Faisal N. and Fernau, Henning and Mann, Kevin},
  title =	{{Roman Census: Enumerating and Counting Roman Dominating Functions on Graph Classes}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{6:1--6:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.6},
  URN =		{urn:nbn:de:0030-drops-185400},
  doi =		{10.4230/LIPIcs.MFCS.2023.6},
  annote =	{Keywords: special graph classes, counting problems, enumeration problems, domination problems, Roman domination}
}
Document
Counting Computations with Formulae: Logical Characterisations of Counting Complexity Classes

Authors: Antonis Achilleos and Aggeliki Chalki


Abstract
We present quantitative logics with two-step semantics based on the framework of quantitative logics introduced by Arenas et al. (2020) and the two-step semantics defined in the context of weighted logics by Gastin & Monmege (2018). We show that some of the fragments of our logics augmented with a least fixed point operator capture interesting classes of counting problems. Specifically, we answer an open question in the area of descriptive complexity of counting problems by providing logical characterisations of two subclasses of #P, namely SpanL and TotP, that play a significant role in the study of approximable counting problems. Moreover, we define logics that capture FPSPACE and SpanPSPACE, which are counting versions of PSPACE.

Cite as

Antonis Achilleos and Aggeliki Chalki. Counting Computations with Formulae: Logical Characterisations of Counting Complexity Classes. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{achilleos_et_al:LIPIcs.MFCS.2023.7,
  author =	{Achilleos, Antonis and Chalki, Aggeliki},
  title =	{{Counting Computations with Formulae: Logical Characterisations of Counting Complexity Classes}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.7},
  URN =		{urn:nbn:de:0030-drops-185412},
  doi =		{10.4230/LIPIcs.MFCS.2023.7},
  annote =	{Keywords: descriptive complexity, quantitative logics, counting problems, #P}
}
Document
Recognizing H-Graphs - Beyond Circular-Arc Graphs

Authors: Deniz Ağaoğlu Çağırıcı, Onur Çağırıcı, Jan Derbisz, Tim A. Hartmann, Petr Hliněný, Jan Kratochvíl, Tomasz Krawczyk, and Peter Zeman


Abstract
In 1992 Biró, Hujter and Tuza introduced, for every fixed connected graph H, the class of H-graphs, defined as the intersection graphs of connected subgraphs of some subdivision of H. Such classes of graphs are related to many known graph classes: for example, K₂-graphs coincide with interval graphs, K₃-graphs with circular-arc graphs, the union of T-graphs, where T ranges over all trees, coincides with chordal graphs. Recently, quite a lot of research has been devoted to understanding the tractability border for various computational problems, such as recognition or isomorphism testing, in classes of H-graphs for different graphs H. In this work we undertake this research topic, focusing on the recognition problem. Chaplick, Töpfer, Voborník, and Zeman showed an XP-algorithm testing whether a given graph is a T-graph, where the parameter is the size of the tree T. In particular, for every fixed tree T the recognition of T-graphs can be solved in polynomial time. Tucker showed a polynomial time algorithm recognizing K₃-graphs (circular-arc graphs). On the other hand, Chaplick et al. showed also that for every fixed graph H containing two distinct cycles sharing an edge, the recognition of H-graphs is NP-hard. The main two results of this work narrow the gap between the NP-hard and 𝖯 cases of H-graph recognition. First, we show that the recognition of H-graphs is NP-hard when H contains two distinct cycles. On the other hand, we show a polynomial-time algorithm recognizing L-graphs, where L is a graph containing a cycle and an edge attached to it (which we call lollipop graphs). Our work leaves open the recognition problems of M-graphs for every unicyclic graph M different from a cycle and a lollipop.

Cite as

Deniz Ağaoğlu Çağırıcı, Onur Çağırıcı, Jan Derbisz, Tim A. Hartmann, Petr Hliněný, Jan Kratochvíl, Tomasz Krawczyk, and Peter Zeman. Recognizing H-Graphs - Beyond Circular-Arc Graphs. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{agaoglucagirici_et_al:LIPIcs.MFCS.2023.8,
  author =	{A\u{g}ao\u{g}lu \c{C}a\u{g}{\i}r{\i}c{\i}, Deniz and \c{C}a\u{g}{\i}r{\i}c{\i}, Onur and Derbisz, Jan and Hartmann, Tim A. and Hlin\v{e}n\'{y}, Petr and Kratochv{\'\i}l, Jan and Krawczyk, Tomasz and Zeman, Peter},
  title =	{{Recognizing H-Graphs - Beyond Circular-Arc Graphs}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{8:1--8:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.8},
  URN =		{urn:nbn:de:0030-drops-185420},
  doi =		{10.4230/LIPIcs.MFCS.2023.8},
  annote =	{Keywords: H-graphs, Intersection Graphs, Helly Property}
}
Document
Descriptive Complexity for Distributed Computing with Circuits

Authors: Veeti Ahvonen, Damian Heiman, Lauri Hella, and Antti Kuusisto


Abstract
We consider distributed algorithms in the realistic scenario where distributed message passing is operated by circuits. We show that within this setting, modal substitution calculus MSC precisely captures the expressive power of circuits. The result is established via constructing translations that are highly efficient in relation to size. We also observe that the coloring algorithm based on Cole-Vishkin can be specified by logarithmic size programs (and thus also logarithmic size circuits) in the bounded-degree scenario.

Cite as

Veeti Ahvonen, Damian Heiman, Lauri Hella, and Antti Kuusisto. Descriptive Complexity for Distributed Computing with Circuits. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{ahvonen_et_al:LIPIcs.MFCS.2023.9,
  author =	{Ahvonen, Veeti and Heiman, Damian and Hella, Lauri and Kuusisto, Antti},
  title =	{{Descriptive Complexity for Distributed Computing with Circuits}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{9:1--9:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.9},
  URN =		{urn:nbn:de:0030-drops-185433},
  doi =		{10.4230/LIPIcs.MFCS.2023.9},
  annote =	{Keywords: Descriptive complexity, distributed computing, logic, graph coloring}
}
Document
Solving Irreducible Stochastic Mean-Payoff Games and Entropy Games by Relative Krasnoselskii-Mann Iteration

Authors: Marianne Akian, Stéphane Gaubert, Ulysse Naepels, and Basile Terver


Abstract
We analyse an algorithm solving stochastic mean-payoff games, combining the ideas of relative value iteration and of Krasnoselskii-Mann damping. We derive parameterized complexity bounds for several classes of games satisfying irreducibility conditions. We show in particular that an ε-approximation of the value of an irreducible concurrent stochastic game can be computed in a number of iterations in O(|log(ε)|) where the constant in the O(⋅) is explicit, depending on the smallest non-zero transition probabilities. This should be compared with a bound in O(ε^{-1}|log(ε)|) obtained by Chatterjee and Ibsen-Jensen (ICALP 2014) for the same class of games, and to a O(ε^{-1}) bound by Allamigeon, Gaubert, Katz and Skomra (ICALP 2022) for turn-based games. We also establish parameterized complexity bounds for entropy games, a class of matrix multiplication games introduced by Asarin, Cervelle, Degorre, Dima, Horn and Kozyakin. We derive these results by methods of variational analysis, establishing contraction properties of the relative Krasnoselskii-Mann iteration with respect to Hilbert’s semi-norm.

Cite as

Marianne Akian, Stéphane Gaubert, Ulysse Naepels, and Basile Terver. Solving Irreducible Stochastic Mean-Payoff Games and Entropy Games by Relative Krasnoselskii-Mann Iteration. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{akian_et_al:LIPIcs.MFCS.2023.10,
  author =	{Akian, Marianne and Gaubert, St\'{e}phane and Naepels, Ulysse and Terver, Basile},
  title =	{{Solving Irreducible Stochastic Mean-Payoff Games and Entropy Games by Relative Krasnoselskii-Mann Iteration}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{10:1--10:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.10},
  URN =		{urn:nbn:de:0030-drops-185448},
  doi =		{10.4230/LIPIcs.MFCS.2023.10},
  annote =	{Keywords: Stochastic mean-payoff games, concurrent games, entropy games, relative value iteration, Krasnoselskii-Mann fixed point algorithm, Hilbert projective metric}
}
Document
The Geometry of Reachability in Continuous Vector Addition Systems with States

Authors: Shaull Almagor, Arka Ghosh, Tim Leys, and Guillermo A. Pérez


Abstract
We study the geometry of reachability sets of continuous vector addition systems with states (VASS). In particular we establish that they are "almost" Minkowski sums of convex cones and zonotopes generated by the vectors labelling the transitions of the VASS. We use the latter to prove that short so-called linear path schemes suffice as witnesses of reachability in continuous VASS. Then, we give new polynomial-time algorithms for the reachability problem for linear path schemes. Finally, we also establish that enriching the model with zero tests makes the reachability problem intractable already for linear path schemes of dimension two.

Cite as

Shaull Almagor, Arka Ghosh, Tim Leys, and Guillermo A. Pérez. The Geometry of Reachability in Continuous Vector Addition Systems with States. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 11:1-11:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{almagor_et_al:LIPIcs.MFCS.2023.11,
  author =	{Almagor, Shaull and Ghosh, Arka and Leys, Tim and P\'{e}rez, Guillermo A.},
  title =	{{The Geometry of Reachability in Continuous Vector Addition Systems with States}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{11:1--11:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.11},
  URN =		{urn:nbn:de:0030-drops-185457},
  doi =		{10.4230/LIPIcs.MFCS.2023.11},
  annote =	{Keywords: Vector addition system with states, reachability, continuous approximation}
}
Document
Competitive Search in the Line and the Star with Predictions

Authors: Spyros Angelopoulos


Abstract
We study the classic problem of searching for a hidden target in the line and the m-ray star, in a setting in which the searcher has some prediction on the hider’s position. We first focus on the main metric for comparing search strategies under predictions; namely, we give positive and negative results on the consistency-robustness tradeoff, where the performance of the strategy is evaluated at extreme situations in which the prediction is either error-free, or adversarially generated, respectively. For the line, we show tight bounds concerning this tradeoff, under the untrusted advice model, in which the prediction is in the form of a k-bit string which encodes the responses to k binary queries. For the star, we give tight, and near-tight tradeoffs in the positional and the directional models, in which the prediction is related to the position of the target within the star, and to the ray on which the target hides, respectively. Last, for all three prediction models, we show how to generalize our study to a setting in which the performance of the strategy is evaluated as a function of the searcher’s desired tolerance to prediction errors, both in terms of positive and inapproximability results.

Cite as

Spyros Angelopoulos. Competitive Search in the Line and the Star with Predictions. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{angelopoulos:LIPIcs.MFCS.2023.12,
  author =	{Angelopoulos, Spyros},
  title =	{{Competitive Search in the Line and the Star with Predictions}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{12:1--12:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.12},
  URN =		{urn:nbn:de:0030-drops-185464},
  doi =		{10.4230/LIPIcs.MFCS.2023.12},
  annote =	{Keywords: Search problems, line and star search, competitive ratio, predictions, consistency and robustness}
}
Document
Rényi-Ulam Games and Online Computation with Imperfect Advice

Authors: Spyros Angelopoulos and Shahin Kamali


Abstract
We study the nascent setting of online computation with imperfect advice, in which the online algorithm is enhanced by some prediction encoded in the form of an imperfect, and possibly erroneous binary string. The algorithm is oblivious to the advice error, but defines a desired tolerance, namely an upper bound on the number of erroneous advice bits it can tolerate. This is a model that generalizes the Pareto-based advice model, in which the performance of the algorithm is only evaluated at the extreme values of error (namely, if the advice has either no errors, or if it is generated adversarially). It also subsumes the model in which the algorithm elicits a prediction on the online sequence, via imperfect responses to a number of binary queries. In this work, we establish connections between games with a lying responder, also known as Rényi-Ulam games, and the design and analysis of online algorithms with imperfect advice. Specifically, we demonstrate how to obtain upper and lower bounds on the competitive ratio for important online problems such as time-series search, online bidding, and fractional knapsack. Our techniques provide the first lower bounds for online problems in this model. We also highlight and exploit connections between competitive analysis with imperfect advice and fault-tolerance in multiprocessor systems. Last, we show how to waive the dependence on the tolerance parameter, by means of resource augmentation and robustification.

Cite as

Spyros Angelopoulos and Shahin Kamali. Rényi-Ulam Games and Online Computation with Imperfect Advice. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 13:1-13:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{angelopoulos_et_al:LIPIcs.MFCS.2023.13,
  author =	{Angelopoulos, Spyros and Kamali, Shahin},
  title =	{{R\'{e}nyi-Ulam Games and Online Computation with Imperfect Advice}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{13:1--13:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.13},
  URN =		{urn:nbn:de:0030-drops-185474},
  doi =		{10.4230/LIPIcs.MFCS.2023.13},
  annote =	{Keywords: Online computation, R\'{e}nyi-Ulam games, query models, beyond worst-case analysis}
}
Document
Multivariate to Bivariate Reduction for Noncommutative Polynomial Factorization

Authors: Vikraman Arvind and Pushkar S. Joglekar


Abstract
Based on a theorem of Bergman [Cohn, 2006] we show that multivariate noncommutative polynomial factorization is deterministic polynomial-time reducible to the factorization of bivariate noncommutative polynomials. More precisely, we show the following: 1) In the white-box setting, given an n-variate noncommutative polynomial f ∈ 𝔽⟨X⟩ over a field 𝔽 (either a finite field or the rationals) as an arithmetic circuit (or algebraic branching program), computing a complete factorization of f into irreducible factors is deterministic polynomial-time reducible to white-box factorization of a noncommutative bivariate polynomial g ∈ 𝔽⟨x,y⟩; the reduction transforms f into a circuit for g (resp. ABP for g), and given a complete factorization of g (namely, arithmetic circuits (resp. ABPs) for irreducible factors of g) the reduction recovers a complete factorization of f in polynomial time. We also obtain a similar deterministic polynomial-time reduction in the black-box setting. 2) Additionally, we show over the field of rationals that bivariate linear matrix factorization of 4× 4 matrices is at least as hard as factoring square-free integers. This indicates that reducing noncommutative polynomial factorization to linear matrix factorization (as done in [Vikraman Arvind and Pushkar S. Joglekar, 2022]) is unlikely to succeed over the field of rationals even in the bivariate case. In contrast, multivariate linear matrix factorization for 3×3 matrices over rationals is in polynomial time.

Cite as

Vikraman Arvind and Pushkar S. Joglekar. Multivariate to Bivariate Reduction for Noncommutative Polynomial Factorization. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{arvind_et_al:LIPIcs.MFCS.2023.14,
  author =	{Arvind, Vikraman and Joglekar, Pushkar S.},
  title =	{{Multivariate to Bivariate Reduction for Noncommutative Polynomial Factorization}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{14:1--14:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.14},
  URN =		{urn:nbn:de:0030-drops-185480},
  doi =		{10.4230/LIPIcs.MFCS.2023.14},
  annote =	{Keywords: Arithmetic circuits, algebraic branching programs, polynomial factorization, automata, noncommutative polynomial ring}
}
Document
Entropic Risk for Turn-Based Stochastic Games

Authors: Christel Baier, Krishnendu Chatterjee, Tobias Meggendorfer, and Jakob Piribauer


Abstract
Entropic risk (ERisk) is an established risk measure in finance, quantifying risk by an exponential re-weighting of rewards. We study ERisk for the first time in the context of turn-based stochastic games with the total reward objective. This gives rise to an objective function that demands the control of systems in a risk-averse manner. We show that the resulting games are determined and, in particular, admit optimal memoryless deterministic strategies. This contrasts risk measures that previously have been considered in the special case of Markov decision processes and that require randomization and/or memory. We provide several results on the decidability and the computational complexity of the threshold problem, i.e. whether the optimal value of ERisk exceeds a given threshold. In the most general case, the problem is decidable subject to Shanuel’s conjecture. If all inputs are rational, the resulting threshold problem can be solved using algebraic numbers, leading to decidability via a polynomial-time reduction to the existential theory of the reals. Further restrictions on the encoding of the input allow the solution of the threshold problem in NP∩coNP. Finally, an approximation algorithm for the optimal value of ERisk is provided.

Cite as

Christel Baier, Krishnendu Chatterjee, Tobias Meggendorfer, and Jakob Piribauer. Entropic Risk for Turn-Based Stochastic Games. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{baier_et_al:LIPIcs.MFCS.2023.15,
  author =	{Baier, Christel and Chatterjee, Krishnendu and Meggendorfer, Tobias and Piribauer, Jakob},
  title =	{{Entropic Risk for Turn-Based Stochastic Games}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.15},
  URN =		{urn:nbn:de:0030-drops-185491},
  doi =		{10.4230/LIPIcs.MFCS.2023.15},
  annote =	{Keywords: Stochastic games, risk-aware verification}
}
Document
Speed Me up If You Can: Conditional Lower Bounds on Opacity Verification

Authors: Jiří Balun, Tomáš Masopust, and Petr Osička


Abstract
Opacity is a property of privacy and security applications asking whether, given a system model, a passive intruder that makes online observations of system’s behaviour can ascertain some "secret" information of the system. Deciding opacity is a PSpace-complete problem, and hence there are no polynomial-time algorithms to verify opacity under the assumption that PSpace differs from PTime. This assumption, however, gives rise to a question whether the existing exponential-time algorithms are the best possible or whether there are faster, sub-exponential-time algorithms. We show that under the (Strong) Exponential Time Hypothesis, there are no algorithms that would be significantly faster than the existing algorithms. As a by-product, we obtained a new conditional lower bound on the time complexity of deciding universality (and therefore also inclusion and equivalence) for nondeterministic finite automata.

Cite as

Jiří Balun, Tomáš Masopust, and Petr Osička. Speed Me up If You Can: Conditional Lower Bounds on Opacity Verification. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{balun_et_al:LIPIcs.MFCS.2023.16,
  author =	{Balun, Ji\v{r}{\'\i} and Masopust, Tom\'{a}\v{s} and Osi\v{c}ka, Petr},
  title =	{{Speed Me up If You Can: Conditional Lower Bounds on Opacity Verification}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{16:1--16:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.16},
  URN =		{urn:nbn:de:0030-drops-185504},
  doi =		{10.4230/LIPIcs.MFCS.2023.16},
  annote =	{Keywords: Finite automata, opacity, fine-grained complexity}
}
Document
Separating Automatic Relations

Authors: Pablo Barceló, Diego Figueira, and Rémi Morvan


Abstract
We study the separability problem for automatic relations (i.e., relations on finite words definable by synchronous automata) in terms of recognizable relations (i.e., finite unions of products of regular languages). This problem takes as input two automatic relations R and R', and asks if there exists a recognizable relation S that contains R and does not intersect R'. We show this problem to be undecidable when the number of products allowed in the recognizable relation is fixed. In particular, checking if there exists a recognizable relation S with at most k products of regular languages that separates R from R' is undecidable, for each fixed k ⩾ 2. Our proofs reveal tight connections, of independent interest, between the separability problem and the finite coloring problem for automatic graphs, where colors are regular languages.

Cite as

Pablo Barceló, Diego Figueira, and Rémi Morvan. Separating Automatic Relations. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{barcelo_et_al:LIPIcs.MFCS.2023.17,
  author =	{Barcel\'{o}, Pablo and Figueira, Diego and Morvan, R\'{e}mi},
  title =	{{Separating Automatic Relations}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{17:1--17:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.17},
  URN =		{urn:nbn:de:0030-drops-185514},
  doi =		{10.4230/LIPIcs.MFCS.2023.17},
  annote =	{Keywords: Automatic relations, recognizable relations, separability, finite colorability}
}
Document
On the Parameterized Complexity of Computing st-Orientations with Few Transitive Edges

Authors: Carla Binucci, Giuseppe Liotta, Fabrizio Montecchiani, Giacomo Ortali, and Tommaso Piselli


Abstract
Orienting the edges of an undirected graph such that the resulting digraph satisfies some given constraints is a classical problem in graph theory, with multiple algorithmic applications. In particular, an st-orientation orients each edge of the input graph such that the resulting digraph is acyclic, and it contains a single source s and a single sink t. Computing an st-orientation of a graph can be done efficiently, and it finds notable applications in graph algorithms and in particular in graph drawing. On the other hand, finding an st-orientation with at most k transitive edges is more challenging and it was recently proven to be NP-hard already when k = 0. We strengthen this result by showing that the problem remains NP-hard even for graphs of bounded diameter, and for graphs of bounded vertex degree. These computational lower bounds naturally raise the question about which structural parameters can lead to tractable parameterizations of the problem. Our main result is a fixed-parameter tractable algorithm parameterized by treewidth.

Cite as

Carla Binucci, Giuseppe Liotta, Fabrizio Montecchiani, Giacomo Ortali, and Tommaso Piselli. On the Parameterized Complexity of Computing st-Orientations with Few Transitive Edges. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 18:1-18:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{binucci_et_al:LIPIcs.MFCS.2023.18,
  author =	{Binucci, Carla and Liotta, Giuseppe and Montecchiani, Fabrizio and Ortali, Giacomo and Piselli, Tommaso},
  title =	{{On the Parameterized Complexity of Computing st-Orientations with Few Transitive Edges}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{18:1--18:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.18},
  URN =		{urn:nbn:de:0030-drops-185524},
  doi =		{10.4230/LIPIcs.MFCS.2023.18},
  annote =	{Keywords: st-orientations, parameterized complexity, graph drawing}
}
Document
Distributed CONGEST Algorithm for Finding Hamiltonian Paths in Dirac Graphs and Generalizations

Authors: Noy Biton, Reut Levi, and Moti Medina


Abstract
We study the problem of finding a Hamiltonian cycle under the promise that the input graph has a minimum degree of at least n/2, where n denotes the number of vertices in the graph. The classical theorem of Dirac states that such graphs (a.k.a. Dirac graphs) are Hamiltonian, i.e., contain a Hamiltonian cycle. Moreover, finding a Hamiltonian cycle in Dirac graphs can be done in polynomial time in the classical centralized model. This paper presents a randomized distributed CONGEST algorithm that finds w.h.p. a Hamiltonian cycle (as well as maximum matching) within O(log n) rounds under the promise that the input graph is a Dirac graph. This upper bound is in contrast to general graphs in which both the decision and search variants of Hamiltonicity require Ω̃(n²) rounds, as shown by Bachrach et al. [PODC'19]. In addition, we consider two generalizations of Dirac graphs: Ore graphs and Rahman-Kaykobad graphs [IPL'05]. In Ore graphs, the sum of the degrees of every pair of non-adjacent vertices is at least n, and in Rahman-Kaykobad graphs, the sum of the degrees of every pair of non-adjacent vertices plus their distance is at least n+1. We show how our algorithm for Dirac graphs can be adapted to work for these more general families of graphs.

Cite as

Noy Biton, Reut Levi, and Moti Medina. Distributed CONGEST Algorithm for Finding Hamiltonian Paths in Dirac Graphs and Generalizations. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{biton_et_al:LIPIcs.MFCS.2023.19,
  author =	{Biton, Noy and Levi, Reut and Medina, Moti},
  title =	{{Distributed CONGEST Algorithm for Finding Hamiltonian Paths in Dirac Graphs and Generalizations}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.19},
  URN =		{urn:nbn:de:0030-drops-185534},
  doi =		{10.4230/LIPIcs.MFCS.2023.19},
  annote =	{Keywords: the CONGEST model, Hamiltonian Path, Hamiltonian Cycle, Dirac graphs, Ore graphs, graph-algorithms}
}
Document
Locality Theorems in Semiring Semantics

Authors: Clotilde Bizière, Erich Grädel, and Matthias Naaf


Abstract
Semiring semantics of first-order logic generalises classical Boolean semantics by permitting truth values from a commutative semiring, which can model information such as costs or access restrictions. This raises the question to what extent classical model-theoretic properties still apply, and how this depends on the algebraic properties of the semiring. In this paper, we study this question for the classical locality theorems due to Hanf and Gaifman. We prove that Hanf’s locality theorem generalises to all semirings with idempotent operations, but fails for many non-idempotent semirings. We then consider Gaifman normal forms and show that for formulae with free variables, Gaifman’s theorem does not generalise beyond the Boolean semiring. Also for sentences, it fails in the natural semiring and the tropical semiring. Our main result, however, is a constructive proof of the existence of Gaifman normal forms for min-max and lattice semirings. The proof implies a stronger version of Gaifman’s classical theorem in Boolean semantics: every sentence has a Gaifman normal form which does not add negations.

Cite as

Clotilde Bizière, Erich Grädel, and Matthias Naaf. Locality Theorems in Semiring Semantics. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{biziere_et_al:LIPIcs.MFCS.2023.20,
  author =	{Bizi\`{e}re, Clotilde and Gr\"{a}del, Erich and Naaf, Matthias},
  title =	{{Locality Theorems in Semiring Semantics}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{20:1--20:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.20},
  URN =		{urn:nbn:de:0030-drops-185546},
  doi =		{10.4230/LIPIcs.MFCS.2023.20},
  annote =	{Keywords: Semiring semantics, Locality, First-order logic}
}
Document
A Characterisation of Functions Computable in Polynomial Time and Space over the Reals with Discrete Ordinary Differential Equations: Simulation of Turing Machines with Analytic Discrete ODEs

Authors: Manon Blanc and Olivier Bournez


Abstract
We prove that functions over the reals computable in polynomial time can be characterised using discrete ordinary differential equations (ODE), also known as finite differences. We also provide a characterisation of functions computable in polynomial space over the reals. In particular, this covers space complexity, while existing characterisations were only able to cover time complexity, and were restricted to functions over the integers, and we prove that no artificial sign or test function is needed even for time complexity. At a technical level, this is obtained by proving that Turing machines can be simulated with analytic discrete ordinary differential equations. We believe this result opens the way to many applications, as it opens the possibility of programming with ODEs, with an underlying well-understood time and space complexity.

Cite as

Manon Blanc and Olivier Bournez. A Characterisation of Functions Computable in Polynomial Time and Space over the Reals with Discrete Ordinary Differential Equations: Simulation of Turing Machines with Analytic Discrete ODEs. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{blanc_et_al:LIPIcs.MFCS.2023.21,
  author =	{Blanc, Manon and Bournez, Olivier},
  title =	{{A Characterisation of Functions Computable in Polynomial Time and Space over the Reals with Discrete Ordinary Differential Equations: Simulation of Turing Machines with Analytic Discrete ODEs}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{21:1--21:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.21},
  URN =		{urn:nbn:de:0030-drops-185554},
  doi =		{10.4230/LIPIcs.MFCS.2023.21},
  annote =	{Keywords: Discrete ordinary differential equations, Finite Differences, Implicit complexity, Recursion scheme, Ordinary differential equations, Models of computation, Analog Computations}
}
Document
MaxCut Above Guarantee

Authors: Ivan Bliznets and Vladislav Epifanov


Abstract
In this paper, we study the computational complexity of the Maximum Cut problem parameterized above guarantee. Our main result provides a linear kernel for the Maximum Cut problem in connected graphs parameterized above the spanning tree. This kernel significantly improves the previous O(k⁵) kernel given by Madathil, Saurabh, and Zehavi [ToCS 2020]. We also provide subexponential running time algorithms for this problem in special classes of graphs: chordal, split, and co-bipartite. We complete the picture by lower bounds under the assumption of the ETH. Moreover, we initiate a study of the Maximum Cut problem above 2/3|E| lower bound in tripartite graphs.

Cite as

Ivan Bliznets and Vladislav Epifanov. MaxCut Above Guarantee. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 22:1-22:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bliznets_et_al:LIPIcs.MFCS.2023.22,
  author =	{Bliznets, Ivan and Epifanov, Vladislav},
  title =	{{MaxCut Above Guarantee}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{22:1--22:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.22},
  URN =		{urn:nbn:de:0030-drops-185560},
  doi =		{10.4230/LIPIcs.MFCS.2023.22},
  annote =	{Keywords: Tripartite, 3-colorable, chordal, maximum cut, FPT-algorithm, linear kernel}
}
Document
Cryptanalysis of a Generalized Subset-Sum Pseudorandom Generator

Authors: Charles Bouillaguet, Florette Martinez, and Damien Vergnaud


Abstract
We present attacks on a generalized subset-sum pseudorandom generator, which was proposed by von zur Gathen and Shparlinski in 2004. Our attacks rely on a sub-quadratic algorithm for solving a vectorial variant of the 3SUM problem, which is of independent interest. The attacks presented have complexities well below the brute-force attack, making the generators vulnerable. We provide a thorough analysis of the attacks and their complexities and demonstrate their practicality through implementations and experiments.

Cite as

Charles Bouillaguet, Florette Martinez, and Damien Vergnaud. Cryptanalysis of a Generalized Subset-Sum Pseudorandom Generator. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 23:1-23:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bouillaguet_et_al:LIPIcs.MFCS.2023.23,
  author =	{Bouillaguet, Charles and Martinez, Florette and Vergnaud, Damien},
  title =	{{Cryptanalysis of a Generalized Subset-Sum Pseudorandom Generator}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{23:1--23:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.23},
  URN =		{urn:nbn:de:0030-drops-185579},
  doi =		{10.4230/LIPIcs.MFCS.2023.23},
  annote =	{Keywords: Cryptography, pseudo-random generator, subset-sum problem, 3SUM problem, cryptanalysis}
}
Document
The Compositional Structure of Bayesian Inference

Authors: Dylan Braithwaite, Jules Hedges, and Toby St Clere Smithe


Abstract
Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may observe that the inversion of the whole can be computed piecewise in terms of the component processes. We study the structure of this compositional rule, noting that it relates to the lens pattern in functional programming. Working in a suitably general axiomatic presentation of a category of Markov kernels, we see how we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a fibred category. We discuss the compositional nature of this, formulated as a functor on the underlying category and explore how this can used for a more type-driven approach to statistical inference.

Cite as

Dylan Braithwaite, Jules Hedges, and Toby St Clere Smithe. The Compositional Structure of Bayesian Inference. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{braithwaite_et_al:LIPIcs.MFCS.2023.24,
  author =	{Braithwaite, Dylan and Hedges, Jules and St Clere Smithe, Toby},
  title =	{{The Compositional Structure of Bayesian Inference}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{24:1--24:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.24},
  URN =		{urn:nbn:de:0030-drops-185584},
  doi =		{10.4230/LIPIcs.MFCS.2023.24},
  annote =	{Keywords: monoidal categories, probabilistic programming, Bayesian inference}
}
Document
Deterministic Constrained Multilinear Detection

Authors: Cornelius Brand, Viktoriia Korchemna, and Michael Skotnica


Abstract
We extend the algebraic techniques of Brand and Pratt (ICALP'21) for deterministic detection of k-multilinear monomials in a given polynomial with non-negative coefficients to the more general situation of detecting colored k-multilinear monomials that satisfy additional constraints on the multiplicities of the colors appearing in them. Our techniques can be viewed as a characteristic-zero generalization of the algebraic tools developed by Guillemot and Sikora (MFCS'10) and Björklund, Kaski and Kowalik (STACS'13) As applications, we recover the state-of-the-art deterministic algorithms for the Graph Motif problem due to Pinter, Schachnai and Zehavi (MFCS'14), and give new deterministic algorithms for generalizations of certain questions on colored directed spanning trees or bipartite planar matchings running in deterministic time O^∗(4^k), studied originally by Gutin, Reidl, Wahlström and Zehavi (J. Comp. Sys. Sci. 95, '18). Finally, we give improved randomized algorithms for intersecting three and four matroids of rank k in characteristic zero, improving the record bounds of Brand and Pratt (ICALP'21) from O^∗(64^k) and O^∗(256^k), respectively, to O^∗(4^k).

Cite as

Cornelius Brand, Viktoriia Korchemna, and Michael Skotnica. Deterministic Constrained Multilinear Detection. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 25:1-25:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{brand_et_al:LIPIcs.MFCS.2023.25,
  author =	{Brand, Cornelius and Korchemna, Viktoriia and Skotnica, Michael},
  title =	{{Deterministic Constrained Multilinear Detection}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{25:1--25:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.25},
  URN =		{urn:nbn:de:0030-drops-185595},
  doi =		{10.4230/LIPIcs.MFCS.2023.25},
  annote =	{Keywords: Fixed-parameter algorithms, Algebraic algorithms, Motif discovery, Matroid intersection}
}
Document
Rational Verification for Nash and Subgame-Perfect Equilibria in Graph Games

Authors: Léonard Brice, Jean-François Raskin, and Marie van den Bogaard


Abstract
We study a natural problem about rational behaviors in multiplayer non-zero-sum sequential infinite duration games played on graphs: rational verification, that consists in deciding whether all the rational answers to a given strategy satisfy some specification. We give the complexities of that problem for two major concepts of rationality: Nash equilibria and subgame-perfect equilibria, and for three major classes of payoff functions: energy, discounted-sum, and mean-payoff.

Cite as

Léonard Brice, Jean-François Raskin, and Marie van den Bogaard. Rational Verification for Nash and Subgame-Perfect Equilibria in Graph Games. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{brice_et_al:LIPIcs.MFCS.2023.26,
  author =	{Brice, L\'{e}onard and Raskin, Jean-Fran\c{c}ois and van den Bogaard, Marie},
  title =	{{Rational Verification for Nash and Subgame-Perfect Equilibria in Graph Games}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{26:1--26:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.26},
  URN =		{urn:nbn:de:0030-drops-185608},
  doi =		{10.4230/LIPIcs.MFCS.2023.26},
  annote =	{Keywords: Games on graphs, Nash equilibria, subgame-perfect equilibria}
}
Document
On Property Testing of the Binary Rank

Authors: Nader H. Bshouty


Abstract
Let M be an n × m (0,1)-matrix. We define the s-binary rank, denoted as br_s(M), of M as the minimum integer d such that there exist d monochromatic rectangles covering all the 1-entries in the matrix, with each 1-entry being covered by at most s rectangles. When s = 1, this corresponds to the binary rank, denoted as br(M), which is well-known in the literature and has many applications. Let R(M) and C(M) denote the sets of rows and columns of M, respectively. Using the result of Sgall [Jiří Sgall, 1999], we establish that if M has an s-binary rank at most d, then |R(M)| ⋅ |C(M)| ≤ binom(d, ≤ s)2^d, where binom(d, ≤ s) = ∑_{i=0}^s binom(d,i). This bound is tight, meaning that there exists a matrix M' with an s-binary rank of d, for which |R(M')| ⋅ |C(M')| = binom(d, ≤ s)2^d. Using this result, we present novel one-sided adaptive and non-adaptive testers for (0,1)-matrices with an s-binary rank at most d (and exactly d). These testers require Õ(binom(d, ≤ s)2^d/ε) and Õ(binom(d, ≤ s)2^d/ε²) queries, respectively. For a fixed s, this improves upon the query complexity of the tester proposed by Parnas et al. in [Michal Parnas et al., 2021] by a factor of Θ(2^d).

Cite as

Nader H. Bshouty. On Property Testing of the Binary Rank. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bshouty:LIPIcs.MFCS.2023.27,
  author =	{Bshouty, Nader H.},
  title =	{{On Property Testing of the Binary Rank}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{27:1--27:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.27},
  URN =		{urn:nbn:de:0030-drops-185616},
  doi =		{10.4230/LIPIcs.MFCS.2023.27},
  annote =	{Keywords: Property testing, binary rank, Boolean rank}
}
Document
Short Definitions in Constraint Languages

Authors: Jakub Bulín and Michael Kompatscher


Abstract
A first-order formula is called primitive positive (pp) if it only admits the use of existential quantifiers and conjunction. Pp-formulas are a central concept in (fixed-template) constraint satisfaction since CSP(Γ) can be viewed as the problem of deciding the primitive positive theory of Γ, and pp-definability captures gadget reductions between CSPs. An important class of tractable constraint languages Γ is characterized by having few subpowers, that is, the number of n-ary relations pp-definable from Γ is bounded by 2^p(n) for some polynomial p(n). In this paper we study a restriction of this property, stating that every pp-definable relation is definable by a pp-formula of polynomial length. We conjecture that the existence of such short definitions is actually equivalent to Γ having few subpowers, and verify this conjecture for a large subclass that, in particular, includes all constraint languages on three-element domains. We furthermore discuss how our conjecture imposes an upper complexity bound of co-NP on the subpower membership problem of algebras with few subpowers.

Cite as

Jakub Bulín and Michael Kompatscher. Short Definitions in Constraint Languages. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 28:1-28:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bulin_et_al:LIPIcs.MFCS.2023.28,
  author =	{Bul{\'\i}n, Jakub and Kompatscher, Michael},
  title =	{{Short Definitions in Constraint Languages}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{28:1--28:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.28},
  URN =		{urn:nbn:de:0030-drops-185629},
  doi =		{10.4230/LIPIcs.MFCS.2023.28},
  annote =	{Keywords: constraint satisfaction, primitive positive definability, few subpowers, polynomially expressive, relational clone, subpower membership}
}
Document
The Online Simple Knapsack Problem with Reservation and Removability

Authors: Elisabet Burjons, Matthias Gehnen, Henri Lotze, Daniel Mock, and Peter Rossmanith


Abstract
In the online simple knapsack problem, a knapsack of unit size 1 is given and an algorithm is tasked to fill it using a set of items that are revealed one after another. Each item must be accepted or rejected at the time they are presented, and these decisions are irrevocable. No prior knowledge about the set and sequence of items is given. The goal is then to maximize the sum of the sizes of all packed items compared to an optimal packing of all items of the sequence. In this paper, we combine two existing variants of the problem that each extend the range of possible actions for a newly presented item by a new option. The first is removability, in which an item that was previously packed into the knapsack may be finally discarded at any point. The second is reservations, which allows the algorithm to delay the decision on accepting or rejecting a new item indefinitely for a proportional fee relative to the size of the given item. If both removability and reservations are permitted, we show that the competitive ratio of the online simple knapsack problem rises depending on the relative reservation costs. As soon as any nonzero fee has to be paid for a reservation, no online algorithm can be better than 1.5-competitive. With rising reservation costs, this competitive ratio increases up to the golden ratio (ϕ ≈ 1.618) that is reached for relative reservation costs of 1-√5/3 ≈ 0.254. We provide a matching upper and lower bound for relative reservation costs up to this value. From this point onward, the tight bound by Iwama and Taketomi for the removable knapsack problem is the best possible competitive ratio, not using any reservations.

Cite as

Elisabet Burjons, Matthias Gehnen, Henri Lotze, Daniel Mock, and Peter Rossmanith. The Online Simple Knapsack Problem with Reservation and Removability. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 29:1-29:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{burjons_et_al:LIPIcs.MFCS.2023.29,
  author =	{Burjons, Elisabet and Gehnen, Matthias and Lotze, Henri and Mock, Daniel and Rossmanith, Peter},
  title =	{{The Online Simple Knapsack Problem with Reservation and Removability}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{29:1--29:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.29},
  URN =		{urn:nbn:de:0030-drops-185635},
  doi =		{10.4230/LIPIcs.MFCS.2023.29},
  annote =	{Keywords: online algorithm, knapsack, competitive ratio, reservation, preemption}
}
Document
Parikh One-Counter Automata

Authors: Michaël Cadilhac, Arka Ghosh, Guillermo A. Pérez, and Ritam Raha


Abstract
Counting abilities in finite automata are traditionally provided by two orthogonal extensions: adding a single counter that can be tested for zeroness at any point, or adding ℤ-valued counters that are tested for equality only at the end of runs. In this paper, finite automata extended with both types of counters are introduced. They are called Parikh One-Counter Automata (POCA): the "Parikh" part referring to the evaluation of counters at the end of runs, and the "One-Counter" part to the single counter that can be tested during runs. Their expressiveness, in the deterministic and nondeterministic variants, is investigated; it is shown in particular that there are deterministic POCA languages that cannot be expressed without nondeterminism in the original models. The natural decision problems are also studied; strikingly, most of them are no harder than in the original models. A parametric version of nonemptiness is also considered.

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Michaël Cadilhac, Arka Ghosh, Guillermo A. Pérez, and Ritam Raha. Parikh One-Counter Automata. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 30:1-30:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{cadilhac_et_al:LIPIcs.MFCS.2023.30,
  author =	{Cadilhac, Micha\"{e}l and Ghosh, Arka and P\'{e}rez, Guillermo A. and Raha, Ritam},
  title =	{{Parikh One-Counter Automata}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{30:1--30:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.30},
  URN =		{urn:nbn:de:0030-drops-185645},
  doi =		{10.4230/LIPIcs.MFCS.2023.30},
  annote =	{Keywords: Parikh automata, Context-free languages, One-counter automata}
}