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Finitely Tractable Promise Constraint Satisfaction Problems
[article]
2020
arXiv
pre-print
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cases in the dichotomy theorem for symmetric Boolean PCSPs allowing negations by Brakensiek and Guruswami [SODA'18]. ...
The Promise Constraint Satisfaction Problem (PCSP) is a generalization of the Constraint Satisfaction Problem (CSP) that includes approximation variants of satisfiability and graph coloring problems. ...
Is it so for all symmetric Boolean templates? For general Boolean templates, the answer is "No": [12] presents an example that requires a three-element C. ...
arXiv:2010.04618v1
fatcat:zezjn7ux6nappp3op6fnu6geqy
Promise Constraint Satisfaction: Algebraic Structure and a Symmetric Boolean Dichotomy
[article]
2021
arXiv
pre-print
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2017 pre-print arXiv:1704.01937v1 fatcat:xi7bthoilvavdmiwx4abxho4qm
A classic result due to Schaefer (1978) classifies all constraint satisfaction problems (CSPs) over the Boolean domain as being either in 𝖯 or 𝖭𝖯-hard. ...
Such insights call us to question the existence of a general dichotomy for Boolean PCSPs. ...
In this work we are interested in a potential complexity dichotomy for promise constraint satisfaction problems (PCSPs). ...
arXiv:1704.01937v2
fatcat:iwsddj3pvnedrotkrksgl5l4du
Algebraic approach to promise constraint satisfaction
[article]
2019
arXiv
pre-print
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2018 pre-print arXiv:1811.00970v1 fatcat:cml2sebvu5foto2ymthgiwwz2yOther Versions
The complexity and approximability of the constraint satisfaction problem (CSP) has been actively studied over the last 20 years. ...
A new version of the CSP, the promise CSP (PCSP) has recently been proposed, motivated by open questions about the approximability of variants of satisfiability and graph colouring. ...
Acknowledgements We would like to thank Libor Barto, Mirek Olšák, Alex Kazda, Josh Brakensiek, Venkat Guruswami, Erkko Lehtonen, and Marcello Mamino for valuable discussions. ...
arXiv:1811.00970v3
fatcat:r2pgvc74ffcxzec6fqdkwvznm4
Symmetric Promise Constraint Satisfaction Problems: Beyond the Boolean Case
[article]
2020
arXiv
pre-print
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The Promise Constraint Satisfaction Problem (PCSP) is a recently introduced vast generalization of the Constraint Satisfaction Problem (CSP). ...
by a ternary symmetric relation. ...
Introduction The Constraint Satisfaction Problem (CSP) over a finite relational structure A (also called a template), denoted CSP(A), can be defined as a homomorphism problem with a fixed target structure ...
arXiv:2010.04623v1
fatcat:yrmqlyq36rbcpn7vsuxebfxgyy
Topology and adjunction in promise constraint satisfaction
[article]
2020
arXiv
pre-print
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This problem naturally generalises to promise graph homomorphism and further to promise constraint satisfaction problems. Complexity analysis of all these problems is notoriously difficult. ...
We apply these techniques, together with the previously introduced algebraic approach, to obtain new NP-hardness results for a significant class of approximate graph colouring and promise graph homomorphism ...
We remark that the above proposition and its proof generalizes to arbitrary Hom complexes Hom(H, G) with the action of Aut(H), more precisely, the complex Hom prod (H, G) (as de ned in [Koz08, De nition ...
arXiv:2003.11351v2
fatcat:w45dasesbbgtbbfhhbboipadry
The Power of the Combined Basic Linear Programming and Affine Relaxation for Promise Constraint Satisfaction Problems
2020
SIAM journal on computing (Print)
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In the field of constraint satisfaction problems (CSPs), promise CSPs are an exciting new direction of study. ...
In a promise CSP, each constraint comes in two forms:"strict"" and"weak,"" and in the associated decision problem one must distinguish between being able to satisfy all the strict constraints versus not ...
We thank Libor Barto, Andrei Krokhin, and Jakub Opr\v sal for useful comments and encouragement. We also thank anonymous reviewers for many helpful comments. ...
doi:10.1137/20m1312745
fatcat:hd7moxv3crbkbeulczbttxv7am
All or nothing: toward a promise problem dichotomy for constraint problems
[article]
2017
arXiv
pre-print
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We show that intractability of the constraint satisfaction problem CSP(R) can, in all known cases, be replaced by an infinite hierarchy of intractable promise problems of increasingly disparate promise ...
A finite constraint language R is a finite set of relations over some finite domain A. ...
The promise conditions include satisfaction as a special case, and complement the promise condition on NO instances provided by the PCP Theorem [3] (at least ε proportion of the constraints must fail ...
arXiv:1611.00886v3
fatcat:p2z7sjjmgzdyrgzt7xmtl2sdne
All or Nothing: Toward a Promise Problem Dichotomy for Constraint Problems
[chapter]
2017
Lecture Notes in Computer Science
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We show that intractability of the constraint satisfaction problem CSP(R) can, in all known cases, be replaced by an infinite hierarchy of intractable promise problems of increasingly disparate promise ...
A finite constraint language R is a finite set of relations over some finite domain A. ...
The promise conditions include satisfaction as a special case, and complement the promise condition on NO instances provided by the PCP Theorem [3] (at least ε proportion of the constraints must fail ...
doi:10.1007/978-3-319-66158-2_10
fatcat:4yjuuspi45aldejfbo527cd4fq
The Constraint Satisfaction Problem: Complexity and Approximability (Dagstuhl Seminar 18231)
2018
Dagstuhl Reports
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Constraint satisfaction has always played a central role in computational complexity theory; appropriate versions of CSPs are classical complete problems for most standard complexity classes. ...
CSPs constitute a very rich and yet sufficiently manageable class of problems to give a good perspective on general computational phenomena. ...
-The Constraint Satisfaction Problem: Complexity and Approximability
From Weak to Strong LP Gaps for all CSPs We study the approximability of constraint satisfaction problems (CSPs) by linear programming ...
doi:10.4230/dagrep.8.6.1
dblp:journals/dagstuhl-reports/GroheGZ18
fatcat:3bqo62ly3rgzlnh3bmkvwbuwea
Constraint Satisfaction Problems over Finite Structures
[article]
2021
arXiv
pre-print
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We initiate a systematic study of the computational complexity of the Constraint Satisfaction Problem (CSP) over finite structures that may contain both relations and operations. ...
leads to a richer theory. ...
Constraint Satisfaction Problems. ...
arXiv:2010.04958v2
fatcat:osswdtu2zrbatjkodmvw4dyg74
Finitely Tractable Promise Constraint Satisfaction Problems
2021
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cases in the dichotomy theorem for symmetric Boolean PCSPs allowing negations by Brakensiek and Guruswami [SODA'18]. ...
The Promise Constraint Satisfaction Problem (PCSP) is a generalization of the Constraint Satisfaction Problem (CSP) that includes approximation variants of satisfiability and graph coloring problems. ...
A doubly cyclic function t : A p 2 → B is b-bounded if
Finitely Tractable Promise Constraint Satisfaction Problems The promised necessary condition for finite tractability is now a simple consequence ...
doi:10.4230/lipics.mfcs.2021.11
fatcat:drl5nugo7bb6jacbrvbixmbrea
Constraint Satisfaction Problems with Infinite Templates
[chapter]
2008
Lecture Notes in Computer Science
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We close with a series of open problems and promising directions of future research. ...
Allowing templates with infinite domains greatly expands the range of problems that can be formulated as a non-uniform constraint satisfaction problem. ...
I would like to thank the referee for his critical and helpful comments, all my CSP co-authors for the cooperation: Hubie Chen, Victor Dalmau, Jan Kára, Martin Kutz, Jaroslav Nešetřil, Michael Pinsker, ...
doi:10.1007/978-3-540-92800-3_8
fatcat:tzhsee2mkjhy5bk7i5jmpiraee
Universal algebra and hardness results for constraint satisfaction problems
2009
Theoretical Computer Science
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and database theory. ...
We present algebraic conditions on constraint languages Γ that ensure the hardness of the constraint satisfaction problem CSP(Γ ) for complexity classes L, NL, P, NP and Mod p L. ...
We are also grateful to the organizers of the Dagstuhl Seminar on the Complexity of Constraints where much of this work was completed. ...
doi:10.1016/j.tcs.2008.12.048
fatcat:qm6drmlez5cy3iqz6xv5cvjazi
Complexity Classification in Infinite-Domain Constraint Satisfaction
[article]
2019
arXiv
pre-print
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A constraint satisfaction problem (CSP) is a computational problem where the input consists of a finite set of variables and a finite set of constraints, and where the task is to decide whether there exists ...
Many problems from areas that have so far seen no interaction with constraint satisfaction theory can be formulated using infinite domains, e.g. problems from temporal and spatial reasoning, phylogenetic ...
Even though very powerful partial results on the dichotomy conjecture have been obtained in recent years, the impact of constraint satisfaction complexity theory on other fields in theoretical computer ...
arXiv:1201.0856v10
fatcat:t32gozkmqrauze2gzqn2ze5kaa
The Complexity of Homomorphisms of Signed Graphs and Signed Constraint Satisfaction
[chapter]
2014
Lecture Notes in Computer Science
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We also introduce the more general concept of signed constraint satisfaction problems and show that a dichotomy for such problems is equivalent to the statement of the Feder-Vardi Dichotomy Conjecture. ...
Extending the notion of usual graph homomorphisms, homomorphisms of signed graphs were introduced, and have lead to some extensions and strengthenings in the theory of graph colorings and homomorphisms ...
We then prove that a complexity dichotomy for the class of signed constraint satisfaction problems exists if and only if Feder-Vardi's celebrated dichotomy conjecture holds. ...
doi:10.1007/978-3-642-54423-1_46
fatcat:cudazm72vre5pjgoq3c24revui
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