27 Search Results for "Siebertz, Sebastian"


Document
Remarks on Parikh-Recognizable Omega-languages

Authors: Mario Grobler, Leif Sabellek, and Sebastian Siebertz

Published in: LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)


Abstract
Several variants of Parikh automata on infinite words were recently introduced by Guha et al. [FSTTCS, 2022]. We show that one of these variants coincides with blind counter machine as introduced by Fernau and Stiebe [Fundamenta Informaticae, 2008]. Fernau and Stiebe showed that every ω-language recognized by a blind counter machine is of the form ⋃_iU_iV_i^ω for Parikh recognizable languages U_i, V_i, but blind counter machines fall short of characterizing this class of ω-languages. They posed as an open problem to find a suitable automata-based characterization. We introduce several additional variants of Parikh automata on infinite words that yield automata characterizations of classes of ω-language of the form ⋃_iU_iV_i^ω for all combinations of languages U_i, V_i being regular or Parikh-recognizable. When both U_i and V_i are regular, this coincides with Büchi’s classical theorem. We study the effect of ε-transitions in all variants of Parikh automata and show that almost all of them admit ε-elimination. Finally we study the classical decision problems with applications to model checking.

Cite as

Mario Grobler, Leif Sabellek, and Sebastian Siebertz. Remarks on Parikh-Recognizable Omega-languages. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 31:1-31:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{grobler_et_al:LIPIcs.CSL.2024.31,
  author =	{Grobler, Mario and Sabellek, Leif and Siebertz, Sebastian},
  title =	{{Remarks on Parikh-Recognizable Omega-languages}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{31:1--31:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.31},
  URN =		{urn:nbn:de:0030-drops-196743},
  doi =		{10.4230/LIPIcs.CSL.2024.31},
  annote =	{Keywords: Parikh automata, blind counter machines, infinite words, B\"{u}chi’s theorem}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Indiscernibles and Flatness in Monadically Stable and Monadically NIP Classes

Authors: Jan Dreier, Nikolas Mählmann, Sebastian Siebertz, and Szymon Toruńczyk

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


Abstract
Monadically stable and monadically NIP classes of structures were initially studied in the context of model theory and defined in logical terms. They have recently attracted attention in the area of structural graph theory, as they generalize notions such as nowhere denseness, bounded cliquewidth, and bounded twinwidth. Our main result is the - to the best of our knowledge first - purely combinatorial characterization of monadically stable classes of graphs, in terms of a property dubbed flip-flatness. A class C of graphs is flip-flat if for every fixed radius r, every sufficiently large set of vertices of a graph G ∈ C contains a large subset of vertices with mutual distance larger than r, where the distance is measured in some graph G' that can be obtained from G by performing a bounded number of flips that swap edges and non-edges within a subset of vertices. Flip-flatness generalizes the notion of uniform quasi-wideness, which characterizes nowhere dense classes and had a key impact on the combinatorial and algorithmic treatment of nowhere dense classes. To obtain this result, we develop tools that also apply to the more general monadically NIP classes, based on the notion of indiscernible sequences from model theory. We show that in monadically stable and monadically NIP classes indiscernible sequences impose a strong combinatorial structure on their definable neighborhoods. All our proofs are constructive and yield efficient algorithms.

Cite as

Jan Dreier, Nikolas Mählmann, Sebastian Siebertz, and Szymon Toruńczyk. Indiscernibles and Flatness in Monadically Stable and Monadically NIP Classes. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 125:1-125:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{dreier_et_al:LIPIcs.ICALP.2023.125,
  author =	{Dreier, Jan and M\"{a}hlmann, Nikolas and Siebertz, Sebastian and Toru\'{n}czyk, Szymon},
  title =	{{Indiscernibles and Flatness in Monadically Stable and Monadically NIP Classes}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{125:1--125:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.125},
  URN =		{urn:nbn:de:0030-drops-181779},
  doi =		{10.4230/LIPIcs.ICALP.2023.125},
  annote =	{Keywords: stability, NIP, combinatorial characterization, first-order model checking}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Flipper Games for Monadically Stable Graph Classes

Authors: Jakub Gajarský, Nikolas Mählmann, Rose McCarty, Pierre Ohlmann, Michał Pilipczuk, Wojciech Przybyszewski, Sebastian Siebertz, Marek Sokołowski, and Szymon Toruńczyk

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


Abstract
A class of graphs C is monadically stable if for every unary expansion Ĉ of C, one cannot encode - using first-order transductions - arbitrarily long linear orders in graphs from C. It is known that nowhere dense graph classes are monadically stable; these include classes of bounded maximum degree and classes that exclude a fixed topological minor. On the other hand, monadic stability is a property expressed in purely model-theoretic terms that is also suited for capturing structure in dense graphs. In this work we provide a characterization of monadic stability in terms of the Flipper game: a game on a graph played by Flipper, who in each round can complement the edge relation between any pair of vertex subsets, and Localizer, who in each round is forced to restrict the game to a ball of bounded radius. This is an analog of the Splitter game, which characterizes nowhere dense classes of graphs (Grohe, Kreutzer, and Siebertz, J. ACM '17). We give two different proofs of our main result. The first proof is based on tools borrowed from model theory, and it exposes an additional property of monadically stable graph classes that is close in spirit to definability of types. Also, as a byproduct, we show that monadic stability for graph classes coincides with monadic stability of existential formulas with two free variables, and we provide another combinatorial characterization of monadic stability via forbidden patterns. The second proof relies on the recently introduced notion of flip-flatness (Dreier, Mählmann, Siebertz, and Toruńczyk, arXiv 2206.13765) and provides an efficient algorithm to compute Flipper’s moves in a winning strategy.

Cite as

Jakub Gajarský, Nikolas Mählmann, Rose McCarty, Pierre Ohlmann, Michał Pilipczuk, Wojciech Przybyszewski, Sebastian Siebertz, Marek Sokołowski, and Szymon Toruńczyk. Flipper Games for Monadically Stable Graph Classes. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 128:1-128:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{gajarsky_et_al:LIPIcs.ICALP.2023.128,
  author =	{Gajarsk\'{y}, Jakub and M\"{a}hlmann, Nikolas and McCarty, Rose and Ohlmann, Pierre and Pilipczuk, Micha{\l} and Przybyszewski, Wojciech and Siebertz, Sebastian and Soko{\l}owski, Marek and Toru\'{n}czyk, Szymon},
  title =	{{Flipper Games for Monadically Stable Graph Classes}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{128:1--128:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.128},
  URN =		{urn:nbn:de:0030-drops-181804},
  doi =		{10.4230/LIPIcs.ICALP.2023.128},
  annote =	{Keywords: Stability theory, structural graph theory, games}
}
Document
Combinatorial and Algorithmic Aspects of Monadic Stability

Authors: Jan Dreier, Nikolas Mählmann, Amer E. Mouawad, Sebastian Siebertz, and Alexandre Vigny

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)


Abstract
Nowhere dense classes of graphs are classes of sparse graphs with rich structural and algorithmic properties, however, they fail to capture even simple classes of dense graphs. Monadically stable classes, originating from model theory, generalize nowhere dense classes and close them under transductions, i.e. transformations defined by colorings and simple first-order interpretations. In this work we aim to extend some combinatorial and algorithmic properties of nowhere dense classes to monadically stable classes of finite graphs. We prove the following results. - For every monadically stable class C and fixed integer s ≥ 3, the Ramsey numbers R_C(s,t) are bounded from above by 𝒪(t^{s-1-δ}) for some δ > 0, improving the bound R(s,t) ∈ 𝒪(t^{s-1}/(log t)^{s-1}) known for the class of all graphs and the bounds known for k-stable graphs when s ≤ k. - For every monadically stable class C and every integer r, there exists δ > 0 such that every graph G ∈ C that contains an r-subdivision of the biclique K_{t,t} as a subgraph also contains K_{t^δ,t^δ} as a subgraph. This generalizes earlier results for nowhere dense graph classes. - We obtain a stronger regularity lemma for monadically stable classes of graphs. - Finally, we show that we can compute polynomial kernels for the independent set and dominating set problems in powers of nowhere dense classes. Formerly, only fixed-parameter tractable algorithms were known for these problems on powers of nowhere dense classes.

Cite as

Jan Dreier, Nikolas Mählmann, Amer E. Mouawad, Sebastian Siebertz, and Alexandre Vigny. Combinatorial and Algorithmic Aspects of Monadic Stability. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{dreier_et_al:LIPIcs.ISAAC.2022.11,
  author =	{Dreier, Jan and M\"{a}hlmann, Nikolas and Mouawad, Amer E. and Siebertz, Sebastian and Vigny, Alexandre},
  title =	{{Combinatorial and Algorithmic Aspects of Monadic Stability}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.11},
  URN =		{urn:nbn:de:0030-drops-172961},
  doi =		{10.4230/LIPIcs.ISAAC.2022.11},
  annote =	{Keywords: Monadic Stability, Structural Graph Theory, Ramsey Numbers, Regularity, Kernels}
}
Document
PACE Solver Description
PACE Solver Description: GraPA-JAVA

Authors: Moritz Bergenthal, Jona Dirks, Thorben Freese, Jakob Gahde, Enna Gerhard, Mario Grobler, and Sebastian Siebertz

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)


Abstract
We present an exact solver for the DFVS, submitted for the exact track of the Parameterized Algorithms and Computational Experiments challenge (PACE) in 2022. The solver heavily relies on data reduction (known from the literature and new reduction rules). The instances are then further processed by integer linear programming approaches. We implemented the algorithm in the scope of a student project at the University of Bremen.

Cite as

Moritz Bergenthal, Jona Dirks, Thorben Freese, Jakob Gahde, Enna Gerhard, Mario Grobler, and Sebastian Siebertz. PACE Solver Description: GraPA-JAVA. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 30:1-30:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bergenthal_et_al:LIPIcs.IPEC.2022.30,
  author =	{Bergenthal, Moritz and Dirks, Jona and Freese, Thorben and Gahde, Jakob and Gerhard, Enna and Grobler, Mario and Siebertz, Sebastian},
  title =	{{PACE Solver Description: GraPA-JAVA}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{30:1--30:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.30},
  URN =		{urn:nbn:de:0030-drops-173861},
  doi =		{10.4230/LIPIcs.IPEC.2022.30},
  annote =	{Keywords: complexity theory, parameterized complexity, linear programming, java, directed feedback vertex set, PACE 2022}
}
Document
SAT Backdoors: Depth Beats Size

Authors: Jan Dreier, Sebastian Ordyniak, and Stefan Szeider

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)


Abstract
For several decades, much effort has been put into identifying classes of CNF formulas whose satisfiability can be decided in polynomial time. Classic results are the linear-time tractability of Horn formulas (Aspvall, Plass, and Tarjan, 1979) and Krom (i.e., 2CNF) formulas (Dowling and Gallier, 1984). Backdoors, introduced by Williams, Gomes and Selman (2003), gradually extend such a tractable class to all formulas of bounded distance to the class. Backdoor size provides a natural but rather crude distance measure between a formula and a tractable class. Backdoor depth, introduced by Mählmann, Siebertz, and Vigny (2021), is a more refined distance measure, which admits the utilization of different backdoor variables in parallel. Bounded backdoor size implies bounded backdoor depth, but there are formulas of constant backdoor depth and arbitrarily large backdoor size. We propose FPT approximation algorithms to compute backdoor depth into the classes Horn and Krom. This leads to a linear-time algorithm for deciding the satisfiability of formulas of bounded backdoor depth into these classes. We base our FPT approximation algorithm on a sophisticated notion of obstructions, extending Mählmann et al.’s obstruction trees in various ways, including the addition of separator obstructions. We develop the algorithm through a new game-theoretic framework that simplifies the reasoning about backdoors. Finally, we show that bounded backdoor depth captures tractable classes of CNF formulas not captured by any known method.

Cite as

Jan Dreier, Sebastian Ordyniak, and Stefan Szeider. SAT Backdoors: Depth Beats Size. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 46:1-46:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{dreier_et_al:LIPIcs.ESA.2022.46,
  author =	{Dreier, Jan and Ordyniak, Sebastian and Szeider, Stefan},
  title =	{{SAT Backdoors: Depth Beats Size}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{46:1--46:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.46},
  URN =		{urn:nbn:de:0030-drops-169840},
  doi =		{10.4230/LIPIcs.ESA.2022.46},
  annote =	{Keywords: satisfiability, backdoor (depth)}
}
Document
CSP Beyond Tractable Constraint Languages

Authors: Jan Dreier, Sebastian Ordyniak, and Stefan Szeider

Published in: LIPIcs, Volume 235, 28th International Conference on Principles and Practice of Constraint Programming (CP 2022)


Abstract
The constraint satisfaction problem (CSP) is among the most studied computational problems. While NP-hard, many tractable subproblems have been identified (Bulatov 2017, Zuk 2017). Backdoors, introduced by Williams, Gomes, and Selman (2003), gradually extend such a tractable class to all CSP instances of bounded distance to the class. Backdoor size provides a natural but rather crude distance measure between a CSP instance and a tractable class. Backdoor depth, introduced by Mählmann, Siebertz, and Vigny (2021) for SAT, is a more refined distance measure, which admits the parallel utilization of different backdoor variables. Bounded backdoor size implies bounded backdoor depth, but there are instances of constant backdoor depth and arbitrarily large backdoor size. Dreier, Ordyniak, and Szeider (2022) provided fixed-parameter algorithms for finding backdoors of small depth into the classes of Horn and Krom formulas. In this paper, we consider backdoor depth for CSP. We consider backdoors w.r.t. tractable subproblems C_Γ of the CSP defined by a constraint language Γ, i.e., where all the constraints use relations from the language Γ. Building upon Dreier et al.’s game-theoretic approach and their notion of separator obstructions, we show that for any finite, tractable, semi-conservative constraint language Γ, the CSP is fixed-parameter tractable parameterized by the backdoor depth into C_Γ plus the domain size. With backdoors of low depth, we reach classes of instances that require backdoors of arbitrary large size. Hence, our results strictly generalize several known results for CSP that are based on backdoor size.

Cite as

Jan Dreier, Sebastian Ordyniak, and Stefan Szeider. CSP Beyond Tractable Constraint Languages. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{dreier_et_al:LIPIcs.CP.2022.20,
  author =	{Dreier, Jan and Ordyniak, Sebastian and Szeider, Stefan},
  title =	{{CSP Beyond Tractable Constraint Languages}},
  booktitle =	{28th International Conference on Principles and Practice of Constraint Programming (CP 2022)},
  pages =	{20:1--20:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-240-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{235},
  editor =	{Solnon, Christine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2022.20},
  URN =		{urn:nbn:de:0030-drops-166490},
  doi =		{10.4230/LIPIcs.CP.2022.20},
  annote =	{Keywords: CSP, backdoor depth, constraint language, tractable class, recursive backdoor}
}
Document
Track A: Algorithms, Complexity and Games
Algorithms and Data Structures for First-Order Logic with Connectivity Under Vertex Failures

Authors: Michał Pilipczuk, Nicole Schirrmacher, Sebastian Siebertz, Szymon Toruńczyk, and Alexandre Vigny

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)


Abstract
We introduce a new data structure for answering connectivity queries in undirected graphs subject to batched vertex failures. Precisely, given any graph G and integer parameter k, we can in fixed-parameter time construct a data structure that can later be used to answer queries of the form: "are vertices s and t connected via a path that avoids vertices u₁,…, u_k?" in time 2^𝒪(k). In the terminology of the literature on data structures, this gives the first deterministic data structure for connectivity under vertex failures where for every fixed number of failures, all operations can be performed in constant time. With the aim to understand the power and the limitations of our new techniques, we prove an algorithmic meta theorem for the recently introduced separator logic, which extends first-order logic with atoms for connectivity under vertex failures. We prove that the model-checking problem for separator logic is fixed-parameter tractable on every class of graphs that exclude a fixed topological minor. We also show a weak converse. This implies that from the point of view of parameterized complexity, under standard complexity theoretical assumptions, the frontier of tractability of separator logic is almost exactly delimited by classes excluding a fixed topological minor. The backbone of our proof relies on a decomposition theorem of Cygan, Lokshtanov, Pilipczuk, Pilipczuk, and Saurabh [SICOMP '19], which provides a tree decomposition of a given graph into bags that are unbreakable. Crucially, unbreakability allows to reduce separator logic to plain first-order logic within each bag individually. Guided by this observation, we design our model-checking algorithm using dynamic programming over the tree decomposition, where the transition at each bag amounts to running a suitable model-checking subprocedure for plain first-order logic. This approach is robust enough to provide also an extension to efficient enumeration of answers to a query expressed in separator logic.

Cite as

Michał Pilipczuk, Nicole Schirrmacher, Sebastian Siebertz, Szymon Toruńczyk, and Alexandre Vigny. Algorithms and Data Structures for First-Order Logic with Connectivity Under Vertex Failures. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 102:1-102:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{pilipczuk_et_al:LIPIcs.ICALP.2022.102,
  author =	{Pilipczuk, Micha{\l} and Schirrmacher, Nicole and Siebertz, Sebastian and Toru\'{n}czyk, Szymon and Vigny, Alexandre},
  title =	{{Algorithms and Data Structures for First-Order Logic with Connectivity Under Vertex Failures}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{102:1--102:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.102},
  URN =		{urn:nbn:de:0030-drops-164432},
  doi =		{10.4230/LIPIcs.ICALP.2022.102},
  annote =	{Keywords: Combinatorics and graph theory, Computational applications of logic, Data structures, Fixed-parameter algorithms and complexity, Graph algorithms}
}
Document
Sparsity in Algorithms, Combinatorics and Logic (Dagstuhl Seminar 21391)

Authors: Daniel Král’, Michał Pilipczuk, Sebastian Siebertz, and Blair D. Sullivan

Published in: Dagstuhl Reports, Volume 11, Issue 8 (2022)


Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 21391 "Sparsity in Algorithms, Combinatorics and Logic". The seminar took place in a hybrid format from September 26 - October 1, 2021 and brought together 61 researchers. This report includes a discussion of the motivation of the seminar, presentation of the overall organization, abstracts of talks, and a report from each of the working groups.

Cite as

Daniel Král’, Michał Pilipczuk, Sebastian Siebertz, and Blair D. Sullivan. Sparsity in Algorithms, Combinatorics and Logic (Dagstuhl Seminar 21391). In Dagstuhl Reports, Volume 11, Issue 8, pp. 115-128, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@Article{kral'_et_al:DagRep.11.8.115,
  author =	{Kr\'{a}l’, Daniel and Pilipczuk, Micha{\l} and Siebertz, Sebastian and Sullivan, Blair D.},
  title =	{{Sparsity in Algorithms, Combinatorics and Logic (Dagstuhl Seminar 21391)}},
  pages =	{115--128},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2022},
  volume =	{11},
  number =	{8},
  editor =	{Kr\'{a}l’, Daniel and Pilipczuk, Micha{\l} and Siebertz, Sebastian and Sullivan, Blair D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.11.8.115},
  URN =		{urn:nbn:de:0030-drops-157718},
  doi =		{10.4230/DagRep.11.8.115},
  annote =	{Keywords: Algorithm design, Parameterised complexity, Sparse graphs, Graph decompositions, Model theory}
}
Document
Structural Properties of the First-Order Transduction Quasiorder

Authors: Jaroslav Nešetřil, Patrice Ossona de Mendez, and Sebastian Siebertz

Published in: LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)


Abstract
Logical transductions provide a very useful tool to encode classes of structures inside other classes of structures. In this paper we study first-order (FO) transductions and the quasiorder they induce on infinite classes of finite graphs. Surprisingly, this quasiorder is very complex, though shaped by the locality properties of first-order logic. This contrasts with the conjectured simplicity of the monadic second order (MSO) transduction quasiorder. We first establish a local normal form for FO transductions, which is of independent interest. Then we prove that the quotient partial order is a bounded distributive join-semilattice, and that the subposet of additive classes is also a bounded distributive join-semilattice. The FO transduction quasiorder has a great expressive power, and many well studied class properties can be defined using it. We apply these structural properties to prove, among other results, that FO transductions of the class of paths are exactly perturbations of classes with bounded bandwidth, that the local variants of monadic stability and monadic dependence are equivalent to their (standard) non-local versions, and that the classes with pathwidth at most k, for k ≥ 1 form a strict hierarchy in the FO transduction quasiorder.

Cite as

Jaroslav Nešetřil, Patrice Ossona de Mendez, and Sebastian Siebertz. Structural Properties of the First-Order Transduction Quasiorder. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{nesetril_et_al:LIPIcs.CSL.2022.31,
  author =	{Ne\v{s}et\v{r}il, Jaroslav and Ossona de Mendez, Patrice and Siebertz, Sebastian},
  title =	{{Structural Properties of the First-Order Transduction Quasiorder}},
  booktitle =	{30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
  pages =	{31:1--31:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-218-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{216},
  editor =	{Manea, Florin and Simpson, Alex},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.31},
  URN =		{urn:nbn:de:0030-drops-157514},
  doi =		{10.4230/LIPIcs.CSL.2022.31},
  annote =	{Keywords: Finite model theory, first-order transductions, structural graph theory}
}
Document
First-Order Logic with Connectivity Operators

Authors: Nicole Schirrmacher, Sebastian Siebertz, and Alexandre Vigny

Published in: LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)


Abstract
First-order logic (FO) can express many algorithmic problems on graphs, such as the independent set and dominating set problem parameterized by solution size. On the other hand, FO cannot express the very simple algorithmic question whether two vertices are connected. We enrich FO with connectivity predicates that are tailored to express algorithmic graph properties that are commonly studied in parameterized algorithmics. By adding the atomic predicates conn_k(x,y,z_1,…,z_k) that hold true in a graph if there exists a path between (the valuations of) x and y after (the valuations of) z_1,…,z_k have been deleted, we obtain separator logic FO+conn. We show that separator logic can express many interesting problems such as the feedback vertex set problem and elimination distance problems to first-order definable classes. Denote by FO+conn_k the fragment of separator logic that is restricted to connectivity predicates with at most k+2 variables (that is, at most k deletions). We show that FO+conn_{k+1} is strictly more expressive than FO+conn_k for all k ≥ 0. We then study the limitations of separator logic and prove that it cannot express planarity, and, in particular, not the disjoint paths problem. We obtain the stronger disjoint-paths logic FO+DP by adding the atomic predicates disjoint-paths_k[(x_1,y_1),…,(x_k,y_k)] that evaluate to true if there are internally vertex-disjoint paths between (the valuations of) x_i and y_i for all 1 ≤ i ≤ k. Disjoint-paths logic can express the disjoint paths problem, the problem of (topological) minor containment, the problem of hitting (topological) minors, and many more. Again we show that the fragments FO+DP_k that use predicates for at most k disjoint paths form a strict hierarchy of expressiveness. Finally, we compare the expressive power of the new logics with that of transitive-closure logics and monadic second-order logic.

Cite as

Nicole Schirrmacher, Sebastian Siebertz, and Alexandre Vigny. First-Order Logic with Connectivity Operators. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 34:1-34:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{schirrmacher_et_al:LIPIcs.CSL.2022.34,
  author =	{Schirrmacher, Nicole and Siebertz, Sebastian and Vigny, Alexandre},
  title =	{{First-Order Logic with Connectivity Operators}},
  booktitle =	{30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
  pages =	{34:1--34:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-218-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{216},
  editor =	{Manea, Florin and Simpson, Alex},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.34},
  URN =		{urn:nbn:de:0030-drops-157548},
  doi =		{10.4230/LIPIcs.CSL.2022.34},
  annote =	{Keywords: First-order logic, graph theory, connectivity}
}
Document
PACE Solver Description
PACE Solver Description: PACA-JAVA

Authors: Jona Dirks, Mario Grobler, Roman Rabinovich, Yannik Schnaubelt, Sebastian Siebertz, and Maximilian Sonneborn

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)


Abstract
We describe PACA-JAVA, an algorithm for solving the cluster editing problem submitted for the exact track of the Parameterized Algorithms and Computational Experiments challenge (PACE) in 2021. The algorithm solves the cluster editing problem by applying data-reduction rules, performing a layout heuristic, local search, iterative ILP verification, and branch-and-bound. We implemented the algorithm in the scope of a student project at the University of Bremen.

Cite as

Jona Dirks, Mario Grobler, Roman Rabinovich, Yannik Schnaubelt, Sebastian Siebertz, and Maximilian Sonneborn. PACE Solver Description: PACA-JAVA. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 30:1-30:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{dirks_et_al:LIPIcs.IPEC.2021.30,
  author =	{Dirks, Jona and Grobler, Mario and Rabinovich, Roman and Schnaubelt, Yannik and Siebertz, Sebastian and Sonneborn, Maximilian},
  title =	{{PACE Solver Description: PACA-JAVA}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{30:1--30:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.30},
  URN =		{urn:nbn:de:0030-drops-154138},
  doi =		{10.4230/LIPIcs.IPEC.2021.30},
  annote =	{Keywords: Cluster editing, parameterized complexity, PACE 2021}
}
Document
Recursive Backdoors for SAT

Authors: Nikolas Mählmann, Sebastian Siebertz, and Alexandre Vigny

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


Abstract
A strong backdoor in a formula φ of propositional logic to a tractable class C of formulas is a set B of variables of φ such that every assignment of the variables in B results in a formula from C. Strong backdoors of small size or with a good structure, e.g. with small backdoor treewidth, lead to efficient solutions for the propositional satisfiability problem SAT. In this paper we propose the new notion of recursive backdoors, which is inspired by the observation that in order to solve SAT we can independently recurse into the components that are created by partial assignments of variables. The quality of a recursive backdoor is measured by its recursive backdoor depth. Similar to the concept of backdoor treewidth, recursive backdoors of bounded depth include backdoors of unbounded size that have a certain treelike structure. However, the two concepts are incomparable and our results yield new tractability results for SAT.

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Nikolas Mählmann, Sebastian Siebertz, and Alexandre Vigny. Recursive Backdoors for SAT. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 73:1-73:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{mahlmann_et_al:LIPIcs.MFCS.2021.73,
  author =	{M\"{a}hlmann, Nikolas and Siebertz, Sebastian and Vigny, Alexandre},
  title =	{{Recursive Backdoors for SAT}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{73:1--73:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.73},
  URN =		{urn:nbn:de:0030-drops-145138},
  doi =		{10.4230/LIPIcs.MFCS.2021.73},
  annote =	{Keywords: Propositional satisfiability SAT, Backdoors, Parameterized Algorithms}
}
Document
Invited Talk
First-Order Transductions of Graphs (Invited Talk)

Authors: Patrice Ossona de Mendez

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)


Abstract
This paper is an extended abstract of my STACS 2021 talk "First-order transductions of graphs".

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Patrice Ossona de Mendez. First-Order Transductions of Graphs (Invited Talk). In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 2:1-2:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{ossonademendez:LIPIcs.STACS.2021.2,
  author =	{Ossona de Mendez, Patrice},
  title =	{{First-Order Transductions of Graphs}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{2:1--2:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.2},
  URN =		{urn:nbn:de:0030-drops-136473},
  doi =		{10.4230/LIPIcs.STACS.2021.2},
  annote =	{Keywords: Finite model theory, structural graph theory}
}
Document
On the Parameterized Complexity of Reconfiguration of Connected Dominating Sets

Authors: Daniel Lokshtanov, Amer E. Mouawad, Fahad Panolan, and Sebastian Siebertz

Published in: LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)


Abstract
In a reconfiguration version of a decision problem 𝒬 the input is an instance of 𝒬 and two feasible solutions S and T. The objective is to determine whether there exists a step-by-step transformation between S and T such that all intermediate steps also constitute feasible solutions. In this work, we study the parameterized complexity of the Connected Dominating Set Reconfiguration problem (CDS-R). It was shown in previous work that the Dominating Set Reconfiguration problem (DS-R) parameterized by k, the maximum allowed size of a dominating set in a reconfiguration sequence, is fixed-parameter tractable on all graphs that exclude a biclique K_{d,d} as a subgraph, for some constant d ≥ 1. We show that the additional connectivity constraint makes the problem much harder, namely, that CDS-R is W[1]-hard parameterized by k+𝓁, the maximum allowed size of a dominating set plus the length of the reconfiguration sequence, already on 5-degenerate graphs. On the positive side, we show that CDS-R parameterized by k is fixed-parameter tractable, and in fact admits a polynomial kernel on planar graphs.

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Daniel Lokshtanov, Amer E. Mouawad, Fahad Panolan, and Sebastian Siebertz. On the Parameterized Complexity of Reconfiguration of Connected Dominating Sets. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{lokshtanov_et_al:LIPIcs.IPEC.2020.24,
  author =	{Lokshtanov, Daniel and Mouawad, Amer E. and Panolan, Fahad and Siebertz, Sebastian},
  title =	{{On the Parameterized Complexity of Reconfiguration of Connected Dominating Sets}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{24:1--24:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Cao, Yixin and Pilipczuk, Marcin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.24},
  URN =		{urn:nbn:de:0030-drops-133276},
  doi =		{10.4230/LIPIcs.IPEC.2020.24},
  annote =	{Keywords: reconfiguration, parameterized complexity, connected dominating set, graph structure theory}
}
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