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One of the central problems in the study of parametrized constraint satisfaction problems is the Dichotomy Conjecture by T. Feder and M. Vardi stating that the constraint satisfaction problem (CSP) over a fixed, finite constraint language…

Computational Complexity · Computer Science 2017-12-12 Dejan Delić

We study Constraint Satisfaction Problems (CSPs) in an infinite context. We show that the dichotomy between easy and hard problems -- established already in the finite case -- presents itself as the strength of the corresponding De…

Logic · Mathematics 2024-10-30 Tamás Kátay , László Márton Tóth , Zoltán Vidnyánszky

We give a complexity dichotomy theorem for the counting Constraint Satisfaction Problem (#CSP in short) with complex weights. To this end, we give three conditions for its tractability. Let F be any finite set of complex-valued functions,…

Computational Complexity · Computer Science 2015-03-19 Jin-Yi Cai , Xi Chen

Constraint satisfaction problems (CSPs) for first-order reducts of finitely bounded homogeneous structures form a large class of computational problems that might exhibit a complexity dichotomy, P versus NP-complete. A powerful method to…

Logic · Mathematics 2024-05-13 Manuel Bodirsky , Bertalan Bodor

The Algebraic Dichotomy Conjecture states that the Constraint Satisfaction Problem over a fixed template is solvable in polynomial time if the algebra of polymorphisms associated to the template lies in a Taylor variety, and is NP-complete…

Logic in Computer Science · Computer Science 2015-07-01 Libor Barto , Marcin Kozik

Combinatorial problems stated as Constraint Satisfaction Problems (CSP) are examined. It is shown by example that any algorithm designed for the original CSP, and involving the AllDifferent constraint, has at least the same level of…

Artificial Intelligence · Computer Science 2020-12-15 Geoff Harris

The natural generalization of the Boolean satisfiability problem to optimization problems is the task of determining the maximum number of clauses that can simultaneously be satisfied in a propositional formula in conjunctive normal form.…

Computational Complexity · Computer Science 2022-04-28 Max Bannach , Pamela Fleischmann , Malte Skambath

We study the complexity of Boolean constraint satisfaction problems (CSPs) when the assignment must have Hamming weight in some congruence class modulo M, for various choices of the modulus M. Due to the known classification of tractable…

Computational Complexity · Computer Science 2019-02-14 Joshua Brakensiek , Sivakanth Gopi , Venkatesan Guruswami

Inspired by computational complexity results for the quantified constraint satisfaction problem, we study the clones of idempotent polymorphisms of certain digraph classes. Our first results are two algebraic dichotomy, even "gap",…

Computational Complexity · Computer Science 2015-05-13 Catarina Carvalho , Florent Madelaine , Barnaby Martin

We propose a new formal language for the expressive representation of probabilistic knowledge based on Answer Set Programming (ASP). It allows for the annotation of first-order formulas as well as ASP rules and facts with probabilities and…

Artificial Intelligence · Computer Science 2014-05-06 Matthias Nickles , Alessandra Mileo

Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by…

Neurons and Cognition · Quantitative Biology 2018-01-16 Ueli Rutishauser , Jean-Jacques Slotine , Rodney J. Douglas

Encoding finite linear CSPs as Boolean formulas and solving them by using modern SAT solvers has proven to be highly effective, as exemplified by the award-winning sugar system. We here develop an alternative approach based on ASP. This…

Artificial Intelligence · Computer Science 2013-12-23 Mutsunori Banbara , Martin Gebser , Katsumi Inoue , Torsten Schaub , Takehide Soh , Naoyuki Tamura , Matthias Weise

The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic…

Combinatorics · Mathematics 2016-07-22 Marcel Jackson , Tomasz Kowalski , Todd Niven

It is known that if an algebra of polymorphisms of the constraint language has the Polynomially Generated Powers (PGP) Property then the Quantified CSP can be reduced to the CSP over the same constraint language with constants. The only…

Computational Complexity · Computer Science 2021-10-19 Dmitriy Zhuk

A weighted constraint satisfaction problem (WCSP) is a constraint satisfaction problem in which preferences among solutions can be expressed. Bucket elimination is a complete technique commonly used to solve this kind of constraint…

Artificial Intelligence · Computer Science 2014-01-16 José Enrique Gallardo , Carlos Cotta , Antonio José Fernández

It is well known that the constraint satisfaction problem over general relational structures can be reduced in polynomial time to digraphs. We present a simple variant of such a reduction and use it to show that the algebraic dichotomy…

Computational Complexity · Computer Science 2013-08-05 Jakub Bulin , Dejan Delic , Marcel Jackson , Todd Niven

The CSP of a first-order theory $T$ is the problem of deciding for a given finite set $S$ of atomic formulas whether $T \cup S$ is satisfiable. Let $T_1$ and $T_2$ be two theories with countably infinite models and disjoint signatures.…

Logic · Mathematics 2023-06-22 Manuel Bodirsky , Johannes Greiner

In the maximum constraint satisfaction problem (Max CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given domain to the variables so as to…

Computational Complexity · Computer Science 2007-05-23 Peter Jonsson , Mikael Klasson , Andrei Krokhin

A famous result by Jeavons, Cohen, and Gyssens shows that every constraint satisfaction problem (CSP) where the constraints are preserved by a semi-lattice operation can be solved in polynomial time. This is one of the basic facts for the…

Computational Complexity · Computer Science 2011-11-30 Manuel Bodirsky , Dugald Macpherson , Johan Thapper

Finite-domain constraint satisfaction problems are either solvable by Datalog, or not even expressible in fixed-point logic with counting. The border between the two regimes coincides with an important dichotomy in universal algebra; in…

Logic · Mathematics 2022-06-08 Manuel Bodirsky , Jakub Rydval