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Kernelization of Constraint Satisfaction Problems: A Study through Universal Algebra [article]

Victor Lagerkvist, Magnus Wahlström
2017 arXiv   pre-print
We also study extensions of this towards SAT and CSP problems with kernels with O(n^c) constraints, c>1, based on embeddings into CSP problems preserved by a k-edge operation, k > c.  ...  For the Boolean satisfiability problem (SAT), and the constraint satisfaction problem (CSP), there exist many results concerning upper and lower bounds for kernelizability of specific problems, but it  ...  The Constraint Satisfaction Problem A set of relations Γ is referred to as a constraint language.  ... 
arXiv:1706.05941v1 fatcat:3exvyn3oxzf4lioqs5sed6z4da

Kernelization of Constraint Satisfaction Problems: A Study Through Universal Algebra [chapter]

Victor Lagerkvist, Magnus Wahlström
2017 Lecture Notes in Computer Science  
We also study extensions of this towards SAT and CSP problems with kernels with O(n c ) constraints, c > 1, based on embeddings into CSP problems preserved by a k-edge operation, k ≤ c + 1.  ...  For the Boolean satisfiability problem (SAT), and the constraint satisfaction problem (CSP), there exist many results concerning upper and lower bounds for kernelizability of specific problems, but it  ...  The Constraint Satisfaction Problem A set of relations Γ is referred to as a constraint language.  ... 
doi:10.1007/978-3-319-66158-2_11 fatcat:jbbgfbzzn5fodeao3ponbspgz4

Universal Algebraic Methods for Constraint Satisfaction Problems [article]

Clifford Bergman, William DeMeo
2022 arXiv   pre-print
After substantial progress over the last 15 years, the "algebraic CSP-dichotomy conjecture" reduces to the following: every local constraint satisfaction problem (CSP) associated with a finite idempotent  ...  algebra is tractable if and only if the algebra has a Taylor term operation.  ...  We give a definition of "constraint satisfaction problem" that is convenient for our purposes.  ... 
arXiv:1611.02867v9 fatcat:rcb7e4ld2vgrfl55y6xar323sy

Constraint Satisfaction Problems with Infinite Templates [chapter]

Manuel Bodirsky
2008 Lecture Notes in Computer Science  
Allowing templates with infinite domains greatly expands the range of problems that can be formulated as a non-uniform constraint satisfaction problem.  ...  We then give an introduction to the universal-algebraic approach to infinite-domain constraint satisfaction, and discuss how cores, polymorphism clones, and pseudovarieties can be used to study the computational  ...  One of the most basic temporal reasoning problems is the constraint satisfaction problem of the socalled point algebra.  ... 
doi:10.1007/978-3-540-92800-3_8 fatcat:tzhsee2mkjhy5bk7i5jmpiraee

On the Computational Complexity of Monotone Constraint Satisfaction Problems [chapter]

Miki Hermann, Florian Richoux
2009 Lecture Notes in Computer Science  
J = {(x, y, z, w) ∈ D 4 | (x = y) ∨ (z = w)} in a classical constraint satisfaction problem reduces it to a monotone constraint satisfaction problem. Proposition 2.  ...  Constraint Satisfaction Problems (CSP) constitute a convenient way to capture many combinatorial problems.  ...  We will study monotone constraint satisfaction problems MCSP(S) through sets of functions F satisfying Inv F = S.  ... 
doi:10.1007/978-3-642-00202-1_25 fatcat:oa42nfcj6nbgpdnjbgbzwdrlea

A Constraint Satisfaction Problem Algorithm for Certain 2-Semilattice-over-Edge Algebras [article]

Ian Payne
2016 arXiv   pre-print
In [8], the so called "algebraic approach" to the constraint satisfaction problem was established.  ...  To any fixed, finite relational structure, D, there is an associated decision problem, CSP(D), which is a restricted version of the constraint satisfaction problem.  ...  Constraint satisfaction problems In this section, we will give precise definitions regarding constraint satisfaction problems. Three versions of CSP.  ... 
arXiv:1609.03943v1 fatcat:n2owoy6ynbhonmjtidftczmadu

The Hidden Subgroup Problem for Universal Algebras [article]

Matthew Moore, Taylor Walenczyk
2020 arXiv   pre-print
We propose a generalization of the HSP to include arbitrary algebraic structures and analyze this new problem on powers of 2-element algebras.  ...  In particular, we identify a class of algebras for which the generalized HSP exhibits super-polynomial speedup on a quantum computer compared to a classical one.  ...  The study of cube terms originated with algebraic approach to the Constraint Satisfaction Problem (CSP) in [2] , and the existence of a cube term for A is associated with some quite strong regularity  ... 
arXiv:2001.11298v1 fatcat:m3oxykxz5reorjugfqhxrn7uku

Robust satisfiability of constraint satisfaction problems

Libor Barto, Marcin Kozik
2012 Proceedings of the 44th symposium on Theory of Computing - STOC '12  
An algorithm for a constraint satisfaction problem is called robust if it outputs an assignment satisfying at least (1 − g(ε))-fraction of the constraints given a (1 − ε)-satisfiable instance, where g(  ...  Guruswami and Zhou conjectured a characterization of constraint languages for which the corresponding constraint satisfaction problem admits an efficient robust algorithm.  ...  Universal algebra and hardness results for constraint satisfaction problems. Theor. Comput. Sci., 410:1629-1647, April 2009.[24] Benoit Larose and László Zádori.  ... 
doi:10.1145/2213977.2214061 dblp:conf/stoc/BartoK12 fatcat:xt7isv333fg3fdjuyoygy2udw4

Towards a dichotomy theorem for the counting constraint satisfaction problem

Andrei A. Bulatov, Víctor Dalmau
2007 Information and Computation  
The counting constraint satisfaction problem (#CSP) can be expressed as follows: given a set of variables, a set of values that can be taken by the variables, and a set of constraints specifying some restrictions  ...  This problem can be parametrized by the set of relations that may appear in a constraint. In this paper we start a systematic study of subclasses of the #CSP restricted in this way.  ...  in the study of the decision constraint satisfaction problem [9, 10, 34, 36] .  ... 
doi:10.1016/j.ic.2006.09.005 fatcat:y6qh7are4fgapekyoiiimduu5q

Worst-Case Risk Quantification under Distributional Ambiguity using Kernel Mean Embedding in Moment Problem [article]

Jia-Jie Zhu, Wittawat Jitkrittum, Moritz Diehl, Bernhard Schölkopf
2020 arXiv   pre-print
Specifically, we formulate the generalized moment problem whose ambiguity set (i.e., the moment constraint) is described by constraints in the associated reproducing kernel Hilbert space in a nonparametric  ...  As a concrete application, we numerically test the proposed method in characterizing the worst-case constraint violation probability in the context of a constrained stochastic control system.  ...  Since the embedding is injective if φ is associated with a universal kernel, the conclusion follows. B. Proof of Lemma 2 Proof.  ... 
arXiv:2004.00166v2 fatcat:2icto7waavazrjpawjgtgtaiuu

Commutative idempotent groupoids and the constraint satisfaction problem

Clifford Bergman, David Failing
2015 Algebra Universalis  
for the constraint satisfaction problem over finite algebras from the varieties they define.  ...  It is tacitly assumed that every instance of a constraint satisfaction problem can be encoded as a finite binary string.  ... 
doi:10.1007/s00012-015-0323-6 fatcat:acdbzdlolfd6zoouqlg2ji67xi

A finer reduction of constraint problems to digraphs

Jakub Bulín, Dejan Delic, Marcel Jackson, Todd Niven, Martin Grohe
2015 Logical Methods in Computer Science  
We present a variant of this construction and show that the corresponding constraint satisfaction problem is logspace equivalent to that over A.  ...  It is well known that the constraint satisfaction problem over a general relational structure A is polynomial time equivalent to the constraint problem over some associated digraph.  ...  number of technical issues.  ... 
doi:10.2168/lmcs-11(4:18)2015 fatcat:mcinbnpmebfnvdjqv2bpmrmhdu

Generalized counting constraint satisfaction problems with determinantal circuits

Jason Morton, Jacob Turner
2015 Linear Algebra and its Applications  
Generalized counting constraint satisfaction problems include Holant problems with planarity restrictions; polynomial-time algorithms for such problems include matchgates and matchcircuits, which are based  ...  We introduce the counting problem in monoidal categories and count-preserving functors as a way to study FP subclasses of problems in settings which are generally #P-hard.  ...  P-hard (examples include weighted counting constraint satisfaction problems [4] ).  ... 
doi:10.1016/j.laa.2014.09.050 fatcat:iytkul4pmfatdijarh2klrldba

The Graph Isomorphism Problem (Dagstuhl Seminar 15511)

László Babai, Anuj Dawar, Pascal Schweitzer, Jacobo Torán, Marc Herbstritt
2016 Dagstuhl Reports  
A highlight of the conference was the presentation of a new quasi-polynomial time algorithm for the Graph Isomorphism Problem, providing the first improvement since 1983.  ...  This report documents the program and the outcomes of Dagstuhl Seminar 15511 "The Graph Isomorphism Problem".  ...  On Tinhofer's Linear Programming Approach to Isomorphism Testing Oleg Verbitsky ( Exploring a linear programming approach to Graph Isomorphism, Tinhofer [1] defined the concept of a compact graph: A graph  ... 
doi:10.4230/dagrep.5.12.1 dblp:journals/dagstuhl-reports/BabaiDST15 fatcat:meig4kvcgffnjiq5wpa6wjs6am

Complexity of conservative constraint satisfaction problems

Andrei A. Bulatov
2011 ACM Transactions on Computational Logic  
In a constraint satisfaction problem (CSP) the aim is to find an assignment of values to a given set of variables, subject to specified constraints. The CSP is known to be NP-complete in general.  ...  Restrictions of this type can be studied by considering those constraint languages which contain all possible unary constraints; we call such languages conservative.  ...  Constraint satisfaction problems related to some particular types of conservative constraint languages have already been studied.  ... 
doi:10.1145/1970398.1970400 fatcat:ngcdqhu4vvg43pib6jm3p3gpwa
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