Related papers: The Connectivity of Boolean Satisfiability: No-Con…
Linear network coding transmits data through networks by letting the intermediate nodes combine the messages they receive and forward the combinations towards their destinations. The solvability problem asks whether the demands of all the…
For a constraint satisfaction problem (CSP), a robust satisfaction algorithm is one that outputs an assignment satisfying most of the constraints on instances that are near-satisfiable. It is known that the CSPs that admit efficient robust…
The paper explores the correspondence between balanced incomplete block designs (BIBD) and certain linear CNF formulas by identifying the points of a block design with the clauses of the Boolean formula and blocks with Boolean variables.…
We determine the computational complexity of approximately counting the total weight of variable assignments for every complex-weighted Boolean constraint satisfaction problem (or CSP) with any number of additional unary (i.e., arity 1)…
Building on a result of Larose and Tesson for constraint satisfaction problems (CSP s), we uncover a dichotomy for the quantified constraint satisfaction problem QCSP(B), where B is a finite structure that is a core. Specifically, such…
We investigate (quantifier-free) spatial constraint languages with equality, contact and connectedness predicates as well as Boolean operations on regions, interpreted over low-dimensional Euclidean spaces. We show that the complexity of…
Promise Constraint Satisfaction Problems (PCSP) were proposed recently by Brakensiek and Guruswami arXiv:1704.01937 as a framework to study approximations for Constraint Satisfaction Problems (CSP). Informally a PCSP asks to distinguish…
Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even…
We prove a complexity dichotomy theorem for all non-negative weighted counting Constraint Satisfaction Problems (CSP). This caps a long series of important results on counting problems including unweighted and weighted graph homomorphisms…
We investigate the `local consistency implies global consistency' principle of strict width among structures within the scope of the Bodirsky-Pinsker dichotomy conjecture for infinite-domain Constraint Satisfaction Problems (CSPs). Our main…
Boolean satisfiability problem has applications in various fields. An efficient algorithm to solve satisfiability problem can be used to solve many other problems efficiently. The input of satisfiability problem is a finite set of clauses.…
The CSP (constraint satisfaction problems) is a class of problems deciding whether there exists a homomorphism from an instance relational structure to a target one. The CSP dichotomy is a profound result recently proved by Zhuk (2020, J.…
We study the complexity of the valued constraint satisfaction problem (VCSP) for every valued structure with the domain ${\mathbb Q}$ that is preserved by all order-preserving bijections. Such VCSPs will be called temporal, in analogy to…
We reduce the problem of proving deterministic and nondeterministic Boolean circuit size lower bounds to the analysis of certain two-dimensional combinatorial cover problems. This is obtained by combining results of Razborov (1989),…
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,…
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. Barto [LICS '19] has shown that a…
We study constraint satisfaction problems (CSPs) where the constraint languages are defined by finite automata, giving rise to automata-based CSPs. The key notion is the concept of Automatic Constraint Satisfaction Problem ($AutCSP$), where…
Maximum surjective constraint satisfaction problems (Max-Sur-CSPs) are computational problems where we are given a set of variables denoting values from a finite domain B and a set of constraints on the variables. A solution to such a…
In this paper we prove the Dichotomy Conjecture on the complexity of nonuniform constraint satisfaction problems posed by Feder and Vardi.
Constraint Satisfaction Problems (CSPs) form a broad class of combinatorial problems, which can be formulated as homomorphism problems between relational structures. The CSP dichotomy theorem classifies all such problems over finite domains…