14 Search Results for "Bodirsky, Manuel"

Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.146
Solving Promise Equations over Monoids and Groups

Authors: Alberto Larrauri and Stanislav Živný

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

Abstract
We give a complete complexity classification for the problem of finding a solution to a given system of equations over a fixed finite monoid, given that a solution over a more restricted monoid exists. As a corollary, we obtain a complexity classification for the same problem over groups.
Cite as

Alberto Larrauri and Stanislav Živný. Solving Promise Equations over Monoids and Groups. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 146:1-146:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{larrauri_et_al:LIPIcs.ICALP.2024.146,
  author =	{Larrauri, Alberto and \v{Z}ivn\'{y}, Stanislav},
  title =	{{Solving Promise Equations over Monoids and Groups}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{146:1--146:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.146},
  URN =		{urn:nbn:de:0030-drops-202893},
  doi =		{10.4230/LIPIcs.ICALP.2024.146},
  annote =	{Keywords: constraint satisfaction, promise constraint satisfaction, equations, minions}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.148
An Order out of Nowhere: A New Algorithm for Infinite-Domain {CSP}s

Authors: Antoine Mottet, Tomáš Nagy, and Michael Pinsker

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

Abstract
We consider the problem of satisfiability of sets of constraints in a given set of finite uniform hypergraphs. While the problem under consideration is similar in nature to the problem of satisfiability of constraints in graphs, the classical complexity reduction to finite-domain CSPs that was used in the proof of the complexity dichotomy for such problems cannot be used as a black box in our case. We therefore introduce an algorithmic technique inspired by classical notions from the theory of finite-domain CSPs, and prove its correctness based on symmetries that depend on a linear order that is external to the structures under consideration. Our second main result is a P/NP-complete complexity dichotomy for such problems over many sets of uniform hypergraphs. The proof is based on the translation of the problem into the framework of constraint satisfaction problems (CSPs) over infinite uniform hypergraphs. Our result confirms in particular the Bodirsky-Pinsker conjecture for CSPs of first-order reducts of some homogeneous hypergraphs. This forms a vast generalization of previous work by Bodirsky-Pinsker (STOC'11) and Bodirsky-Martin-Pinsker-Pongrácz (ICALP'16) on graph satisfiability.
Cite as

Antoine Mottet, Tomáš Nagy, and Michael Pinsker. An Order out of Nowhere: A New Algorithm for Infinite-Domain {CSP}s. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 148:1-148:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{mottet_et_al:LIPIcs.ICALP.2024.148,
  author =	{Mottet, Antoine and Nagy, Tom\'{a}\v{s} and Pinsker, Michael},
  title =	{{An Order out of Nowhere: A New Algorithm for Infinite-Domain \{CSP\}s}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{148:1--148:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.148},
  URN =		{urn:nbn:de:0030-drops-202912},
  doi =		{10.4230/LIPIcs.ICALP.2024.148},
  annote =	{Keywords: Constraint Satisfaction Problems, Hypergraphs, Polymorphisms}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.150
Homogeneity and Homogenizability: Hard Problems for the Logic SNP

Authors: Jakub Rydval

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

Abstract
The infinite-domain CSP dichotomy conjecture extends the finite-domain CSP dichotomy theorem to reducts of finitely bounded homogeneous structures. Every countable finitely bounded homogeneous structure is uniquely described by a universal first-order sentence up to isomorphism, and every reduct of such a structure by a sentence of the logic SNP. By Fraïssé’s Theorem, testing the existence of a finitely bounded homogeneous structure for a given universal first-order sentence is equivalent to testing the amalgamation property for the class of its finite models. The present paper motivates a complexity-theoretic view on the classification problem for finitely bounded homogeneous structures. We show that this meta-problem is EXPSPACE-hard or PSPACE-hard, depending on whether the input is specified by a universal sentence or a set of forbidden substructures. By relaxing the input to SNP sentences and the question to the existence of a structure with a finitely bounded homogeneous expansion, we obtain a different meta-problem, closely related to the question of homogenizability. We show that this second meta-problem is already undecidable, even if the input SNP sentence comes from the Datalog fragment and uses at most binary relation symbols. As a byproduct of our proof, we also get the undecidability of some other properties for Datalog programs, e.g., whether they can be rewritten in the logic MMSNP, whether they solve some finite-domain CSP, or whether they define a structure with a homogeneous Ramsey expansion in a finite relational signature.
Cite as

Jakub Rydval. Homogeneity and Homogenizability: Hard Problems for the Logic SNP. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 150:1-150:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{rydval:LIPIcs.ICALP.2024.150,
  author =	{Rydval, Jakub},
  title =	{{Homogeneity and Homogenizability: Hard Problems for the Logic SNP}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{150:1--150:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.150},
  URN =		{urn:nbn:de:0030-drops-202939},
  doi =		{10.4230/LIPIcs.ICALP.2024.150},
  annote =	{Keywords: constraint satisfaction problems, finitely bounded, homogeneous, amalgamation property, universal, SNP, homogenizable}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.151
Identifying Tractable Quantified Temporal Constraints Within Ord-Horn

Authors: Jakub Rydval, Žaneta Semanišinová, and Michał Wrona

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

Abstract
The constraint satisfaction problem, parameterized by a relational structure, provides a general framework for expressing computational decision problems. Already the restriction to the class of all finite structures forms an interesting microcosm on its own, but to express decision problems in temporal reasoning one has to take a step beyond the finite-domain realm. An important class of templates used in this context are temporal structures, i.e., structures over ℚ whose relations are first-order definable using the usual countable dense linear order without endpoints. In the standard setting, which allows only existential quantification over input variables, the complexity of finite and temporal constraints has been fully classified. In the quantified setting, i.e., when one also allows universal quantifiers, there is only a handful of partial classification results and many concrete cases of unknown complexity. This paper presents a significant progress towards understanding the complexity of the quantified constraint satisfaction problem for temporal structures. We provide a complexity dichotomy for quantified constraints over the Ord-Horn fragment, which played an important role in understanding the complexity of constraints both over temporal structures and in Allen’s interval algebra. We show that all problems under consideration are in P or coNP-hard. In particular, we determine the complexity of the quantified constraint satisfaction problem for (ℚ;x = y⇒ x ≥ z), hereby settling a question open for more than ten years.
Cite as

Jakub Rydval, Žaneta Semanišinová, and Michał Wrona. Identifying Tractable Quantified Temporal Constraints Within Ord-Horn. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 151:1-151:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{rydval_et_al:LIPIcs.ICALP.2024.151,
  author =	{Rydval, Jakub and Semani\v{s}inov\'{a}, \v{Z}aneta and Wrona, Micha{\l}},
  title =	{{Identifying Tractable Quantified Temporal Constraints Within Ord-Horn}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{151:1--151:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.151},
  URN =		{urn:nbn:de:0030-drops-202944},
  doi =		{10.4230/LIPIcs.ICALP.2024.151},
  annote =	{Keywords: constraint satisfaction problems, quantifiers, dichotomy, temporal reasoning, Ord-Horn}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2023.116
Network Satisfaction Problems Solved by k-Consistency

Authors: Manuel Bodirsky and Simon Knäuer

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

Abstract
We show that the problem of deciding for a given finite relation algebra A whether the network satisfaction problem for A can be solved by the k-consistency procedure, for some k ∈ ℕ, is undecidable. For the important class of finite relation algebras A with a normal representation, however, the decidability of this problem remains open. We show that if A is symmetric and has a flexible atom, then the question whether NSP(A) can be solved by k-consistency, for some k ∈ ℕ, is decidable (even in polynomial time in the number of atoms of A). This result follows from a more general sufficient condition for the correctness of the k-consistency procedure for finite symmetric relation algebras. In our proof we make use of a result of Alexandr Kazda about finite binary conservative structures.
Cite as

Manuel Bodirsky and Simon Knäuer. Network Satisfaction Problems Solved by k-Consistency. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 116:1-116:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{bodirsky_et_al:LIPIcs.ICALP.2023.116,
  author =	{Bodirsky, Manuel and Kn\"{a}uer, Simon},
  title =	{{Network Satisfaction Problems Solved by k-Consistency}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{116:1--116:20},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.116},
  URN =		{urn:nbn:de:0030-drops-181680},
  doi =		{10.4230/LIPIcs.ICALP.2023.116},
  annote =	{Keywords: Constraint Satisfaction, Computational Complexity, Relation Algebras, Network Satisfaction, Qualitative Reasoning, k-Consistency, Datalog}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2021.120
Datalog-Expressibility for Monadic and Guarded Second-Order Logic

Authors: Manuel Bodirsky, Simon Knäuer, and Sebastian Rudolph

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
We characterise the sentences in Monadic Second-order Logic (MSO) that are over finite structures equivalent to a Datalog program, in terms of an existential pebble game. We also show that for every class C of finite structures that can be expressed in MSO and is closed under homomorphisms, and for all 𝓁,k ∈ , there exists a canonical Datalog program Π of width (𝓁,k), that is, a Datalog program of width (𝓁,k) which is sound for C (i.e., Π only derives the goal predicate on a finite structure 𝔄 if 𝔄 ∈ C) and with the property that Π derives the goal predicate whenever some Datalog program of width (𝓁,k) which is sound for C derives the goal predicate. The same characterisations also hold for Guarded Second-order Logic (GSO), which properly extends MSO. To prove our results, we show that every class C in GSO whose complement is closed under homomorphisms is a finite union of constraint satisfaction problems (CSPs) of ω-categorical structures.
Cite as

Manuel Bodirsky, Simon Knäuer, and Sebastian Rudolph. Datalog-Expressibility for Monadic and Guarded Second-Order Logic. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 120:1-120:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{bodirsky_et_al:LIPIcs.ICALP.2021.120,
  author =	{Bodirsky, Manuel and Kn\"{a}uer, Simon and Rudolph, Sebastian},
  title =	{{Datalog-Expressibility for Monadic and Guarded Second-Order Logic}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{120:1--120:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.120},
  URN =		{urn:nbn:de:0030-drops-141897},
  doi =		{10.4230/LIPIcs.ICALP.2021.120},
  annote =	{Keywords: Monadic Second-order Logic, Guarded Second-order Logic, Datalog, constraint satisfaction, homomorphism-closed, conjunctive query, primitive positive formula, pebble game, \omega-categoricity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2020.39
Relational Width of First-Order Expansions of Homogeneous Graphs with Bounded Strict Width

Authors: Michał Wrona

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)

Abstract
Solving the algebraic dichotomy conjecture for constraint satisfaction problems over structures first-order definable in countably infinite finitely bounded homogeneous structures requires understanding the applicability of local-consistency methods in this setting. We study the amount of consistency (measured by relational width) needed to solve CSP(?) for first-order expansions ? of countably infinite homogeneous graphs ℋ := (A; E), which happen all to be finitely bounded. We study our problem for structures ? that additionally have bounded strict width, i.e., for which establishing local consistency of an instance of CSP(?) not only decides if there is a solution but also ensures that every solution may be obtained from a locally consistent instance by greedily assigning values to variables, without backtracking. Our main result is that the structures ? under consideration have relational width exactly (2, ?_ℋ) where ?_ℋ is the maximal size of a forbidden subgraph of ℋ, but not smaller than 3. It beats the upper bound: (2 m, 3 m) where m = max(arity(?)+1, ?, 3) and arity(?) is the largest arity of a relation in ?, which follows from a sufficient condition implying bounded relational width given in [Manuel Bodirsky and Antoine Mottet, 2018]. Since ?_ℋ may be arbitrarily large, our result contrasts the collapse of the relational bounded width hierarchy for finite structures ?, whose relational width, if finite, is always at most (2,3).
Cite as

Michał Wrona. Relational Width of First-Order Expansions of Homogeneous Graphs with Bounded Strict Width. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 39:1-39:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{wrona:LIPIcs.STACS.2020.39,
  author =	{Wrona, Micha{\l}},
  title =	{{Relational Width of First-Order Expansions of Homogeneous Graphs with Bounded Strict Width}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{39:1--39:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.39},
  URN =		{urn:nbn:de:0030-drops-119000},
  doi =		{10.4230/LIPIcs.STACS.2020.39},
  annote =	{Keywords: Constraint Satisfaction, Homogeneous Graphs, Bounded Width, Strict Width, Relational Width, Computational Complexity}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.12
Submodular Functions and Valued Constraint Satisfaction Problems over Infinite Domains

Authors: Manuel Bodirsky, Marcello Mamino, and Caterina Viola

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
Valued constraint satisfaction problems (VCSPs) are a large class of combinatorial optimisation problems. It is desirable to classify the computational complexity of VCSPs depending on a fixed set of allowed cost functions in the input. Recently, the computational complexity of all VCSPs for finite sets of cost functions over finite domains has been classified in this sense. Many natural optimisation problems, however, cannot be formulated as VCSPs over a finite domain. We initiate the systematic investigation of infinite-domain VCSPs by studying the complexity of VCSPs for piecewise linear homogeneous cost functions. We remark that in this paper the infinite domain will always be the set of rational numbers. We show that such VCSPs can be solved in polynomial time when the cost functions are additionally submodular, and that this is indeed a maximally tractable class: adding any cost function that is not submodular leads to an NP-hard VCSP.
Cite as

Manuel Bodirsky, Marcello Mamino, and Caterina Viola. Submodular Functions and Valued Constraint Satisfaction Problems over Infinite Domains. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{bodirsky_et_al:LIPIcs.CSL.2018.12,
  author =	{Bodirsky, Manuel and Mamino, Marcello and Viola, Caterina},
  title =	{{Submodular Functions and Valued Constraint Satisfaction Problems over Infinite Domains}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{12:1--12:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.12},
  URN =		{urn:nbn:de:0030-drops-96792},
  doi =		{10.4230/LIPIcs.CSL.2018.12},
  annote =	{Keywords: Valued constraint satisfaction problems, Piecewise linear functions, Submodular functions, Semilinear, Constraint satisfaction, Optimisation, Model Theory}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2018.33
The Complexity of Disjunctive Linear Diophantine Constraints

Authors: Manuel Bodirsky, Barnaby Martin, Marcello Mamino, and Antoine Mottet

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
We study the Constraint Satisfaction Problem CSP( A), where A is first-order definable in (Z;+,1) and contains +. We prove such problems are either in P or NP-complete.
Cite as

Manuel Bodirsky, Barnaby Martin, Marcello Mamino, and Antoine Mottet. The Complexity of Disjunctive Linear Diophantine Constraints. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 33:1-33:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{bodirsky_et_al:LIPIcs.MFCS.2018.33,
  author =	{Bodirsky, Manuel and Martin, Barnaby and Mamino, Marcello and Mottet, Antoine},
  title =	{{The Complexity of Disjunctive Linear Diophantine Constraints}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{33:1--33:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.33},
  URN =		{urn:nbn:de:0030-drops-96150},
  doi =		{10.4230/LIPIcs.MFCS.2018.33},
  annote =	{Keywords: Constraint Satisfaction, Presburger Arithmetic, Computational Complexity}
}
Document
DOI: 10.4230/DFU.Vol7.15301.79
Constraint Satisfaction Problems over Numeric Domains

Authors: Manuel Bodirsky and Marcello Mamino

Published in: Dagstuhl Follow-Ups, Volume 7, The Constraint Satisfaction Problem: Complexity and Approximability (2017)

Abstract
We present a survey of complexity results for constraint satisfaction problems (CSPs) over the integers, the rationals, the reals, and the complex numbers. Examples of such problems are feasibility of linear programs, integer linear programming, the max-atoms problem, Hilbert's tenth problem, and many more. Our particular focus is to identify those CSPs that can be solved in polynomial time, and to distinguish them from CSPs that are NP-hard. A very helpful tool for obtaining complexity classifications in this context is the concept of a polymorphism from universal algebra.
Cite as

Manuel Bodirsky and Marcello Mamino. Constraint Satisfaction Problems over Numeric Domains. In The Constraint Satisfaction Problem: Complexity and Approximability. Dagstuhl Follow-Ups, Volume 7, pp. 79-111, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InCollection{bodirsky_et_al:DFU.Vol7.15301.79,
  author =	{Bodirsky, Manuel and Mamino, Marcello},
  title =	{{Constraint Satisfaction Problems over Numeric Domains}},
  booktitle =	{The Constraint Satisfaction Problem: Complexity and Approximability},
  pages =	{79--111},
  series =	{Dagstuhl Follow-Ups},
  ISBN =	{978-3-95977-003-3},
  ISSN =	{1868-8977},
  year =	{2017},
  volume =	{7},
  editor =	{Krokhin, Andrei and Zivny, Stanislav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DFU.Vol7.15301.79},
  URN =		{urn:nbn:de:0030-drops-69580},
  doi =		{10.4230/DFU.Vol7.15301.79},
  annote =	{Keywords: Constraint satisfaction problems, Numerical domains}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.119
Constraint Satisfaction Problems for Reducts of Homogeneous Graphs

Authors: Manuel Bodirsky, Barnaby Martin, Michael Pinsker, and András Pongrácz

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
For n >= 3, let (Hn, E) denote the n-th Henson graph, i.e., the unique countable homogeneous graph with exactly those finite graphs as induced subgraphs that do not embed the complete graph on n vertices. We show that for all structures Gamma with domain Hn whose relations are first-order definable in (Hn, E) the constraint satisfaction problem for Gamma is either in P or is NP-complete. We moreover show a similar complexity dichotomy for all structures whose relations are first-order definable in a homogeneous graph whose reflexive closure is an equivalence relation. Together with earlier results, in particular for the random graph, this completes the complexity classification of constraint satisfaction problems of structures first-order definable in countably infinite homogeneous graphs: all such problems are either in P or NP-complete.
Cite as

Manuel Bodirsky, Barnaby Martin, Michael Pinsker, and András Pongrácz. Constraint Satisfaction Problems for Reducts of Homogeneous Graphs. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 119:1-119:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{bodirsky_et_al:LIPIcs.ICALP.2016.119,
  author =	{Bodirsky, Manuel and Martin, Barnaby and Pinsker, Michael and Pongr\'{a}cz, Andr\'{a}s},
  title =	{{Constraint Satisfaction Problems for Reducts of Homogeneous Graphs}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{119:1--119:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.119},
  URN =		{urn:nbn:de:0030-drops-62543},
  doi =		{10.4230/LIPIcs.ICALP.2016.119},
  annote =	{Keywords: Constraint Satisfaction, Homogeneous Graphs, Computational Complexity, Universal Algebra, Ramsey Theory}
}
Document
DOI: 10.4230/LIPIcs.STACS.2016.20
The Complexity of Phylogeny Constraint Satisfaction

Authors: Manuel Bodirsky, Peter Jonsson, and Trung Van Pham

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

Abstract
We systematically study the computational complexity of a broad class of computational problems in phylogenetic reconstruction. The class contains for example the rooted triple consistency problem, forbidden subtree problems, the quartet consistency problem, and many other problems studied in the bioinformatics literature. The studied problems can be described as constraint satisfaction problems where the constraints have a first-order definition over the rooted triple relation. We show that every such phylogeny problem can be solved in polynomial time or is NP-complete. On the algorithmic side, we generalize a well-known polynomial-time algorithm of Aho, Sagiv, Szymanski, and Ullman for the rooted triple consistency problem. Our algorithm repeatedly solves linear equation systems to construct a solution in polynomial time. We then show that every phylogeny problem that cannot be solved by our algorithm is NP-complete. Our classification establishes a dichotomy for a large class of infinite structures that we believe is of independent interest in universal algebra, model theory, and topology. The proof of our main result combines results and techniques from various research areas: a recent classification of the model-complete cores of the reducts of the homogeneous binary branching C-relation, Leeb’s Ramsey theorem for rooted trees, and universal algebra.
Cite as

Manuel Bodirsky, Peter Jonsson, and Trung Van Pham. The Complexity of Phylogeny Constraint Satisfaction. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 20:1-20:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{bodirsky_et_al:LIPIcs.STACS.2016.20,
  author =	{Bodirsky, Manuel and Jonsson, Peter and Van Pham, Trung},
  title =	{{The Complexity of Phylogeny Constraint Satisfaction}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{20:1--20:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Ollinger, Nicolas and Vollmer, Heribert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.20},
  URN =		{urn:nbn:de:0030-drops-57218},
  doi =		{10.4230/LIPIcs.STACS.2016.20},
  annote =	{Keywords: constraint satisfaction problems, computational complexity, phylogenetic reconstruction, ramsey theory, model theory}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.STACS.2015.2
The Complexity of Constraint Satisfaction Problems (Invited Talk)

Authors: Manuel Bodirsky

Published in: LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)

Abstract
The tractability conjecture for constraint satisfaction problems (CSPs) describes the constraint languages over a finite domain whose CSP can be solved in polynomial-time. The precise formulation of the conjecture uses basic notions from universal algebra. In this talk, we give a short introduction to the universal-algebraic approach to the study of the complexity of CSPs. Finally, we discuss attempts to generalise the tractability conjecture to large classes of constraint languages over infinite domains, in particular for constraint languages that arise in qualitative temporal and spatial reasoning.
Cite as

Manuel Bodirsky. The Complexity of Constraint Satisfaction Problems (Invited Talk). In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 2-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

Copy BibTex To Clipboard

@InProceedings{bodirsky:LIPIcs.STACS.2015.2,
  author =	{Bodirsky, Manuel},
  title =	{{The Complexity of Constraint Satisfaction Problems}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{2--9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Mayr, Ernst W. and Ollinger, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.2},
  URN =		{urn:nbn:de:0030-drops-49567},
  doi =		{10.4230/LIPIcs.STACS.2015.2},
  annote =	{Keywords: constraint satisfaction, universal algebra, model theory, clones, temporal and spatial reasoning}
}
Document
DOI: 10.4230/LIPIcs.CSL.2012.122
Equivalence Constraint Satisfaction Problems

Authors: Manuel Bodirsky and Michal Wrona

Published in: LIPIcs, Volume 16, Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (2012)

Abstract
The following result for finite structures Gamma has been conjectured to hold for all countably infinite omega-categorical structures Gamma: either the model-complete core Delta of Gamma has an expansion by finitely many constants such that the pseudovariety generated by its polymorphism algebra contains a two-element algebra all of whose operations are projections, or there is a homomorphism f from Delta^k to Delta, for some finite k, and an automorphism alpha of Delta satisfying f(x1,...,xk) = alpha(f(x2,...,xk,x1)). This conjecture has been confirmed for all infinite structures Gamma that have a first-order definition over (Q;<), and for all structures that are definable over the random graph. In this paper, we verify the conjecture for all structures that are definable over an equivalence relation with a countably infinite number of countably infinite classes. Our result implies a complexity dichotomy (into NP-complete and P) for a family of constraint satisfaction problems (CSPs) which we call equivalence constraint satisfaction problems. The classification for equivalence CSPs can also be seen as a first step towards a classification of the CSPs for all relational structures that are first-order definable over Allen's interval algebra, a well-known constraint calculus in temporal reasoning.
Cite as

Manuel Bodirsky and Michal Wrona. Equivalence Constraint Satisfaction Problems. In Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 16, pp. 122-136, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

Copy BibTex To Clipboard

@InProceedings{bodirsky_et_al:LIPIcs.CSL.2012.122,
  author =	{Bodirsky, Manuel and Wrona, Michal},
  title =	{{Equivalence Constraint Satisfaction Problems}},
  booktitle =	{Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL},
  pages =	{122--136},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-42-2},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{16},
  editor =	{C\'{e}gielski, Patrick and Durand, Arnaud},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2012.122},
  URN =		{urn:nbn:de:0030-drops-36689},
  doi =		{10.4230/LIPIcs.CSL.2012.122},
  annote =	{Keywords: Constraint satisfaction problems, universal algebra, model theory, Ram- sey theory, temporal reasoning, computational complexity}
}
  • Refine by Author
  • 9 Bodirsky, Manuel
  • 3 Mamino, Marcello
  • 2 Knäuer, Simon
  • 2 Martin, Barnaby
  • 2 Mottet, Antoine
  • Show More...

  • Refine by Classification
  • 3 Theory of computation → Complexity theory and logic
  • 3 Theory of computation → Logic
  • 3 Theory of computation → Problems, reductions and completeness
  • 2 Theory of computation → Computational complexity and cryptography
  • 2 Theory of computation → Finite Model Theory
  • Show More...

  • Refine by Keyword
  • 4 Computational Complexity
  • 4 Constraint Satisfaction
  • 3 constraint satisfaction
  • 3 constraint satisfaction problems
  • 3 model theory
  • Show More...

  • Refine by Type
  • 14 document

  • Refine by Publication Year
  • 4 2024
  • 2 2016
  • 2 2018
  • 1 2012
  • 1 2015
  • Show More...

© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact