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In the field of constraint satisfaction problems (CSP), 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…
While 3-SAT is NP-hard, 2-SAT is solvable in polynomial time. Austrin, Guruswami, and H\r{a}stad roved a result known as "$(2+\varepsilon)$-SAT is NP-hard" [FOCS'14/SICOMP'17]. They showed that the problem of distinguishing k-CNF formulas…
The Shortest Common Supersequence problem (SCS for short) consists in finding a shortest common supersequence of a finite set of words on a fixed alphabet Sigma. It is well-known that its decision version denoted [SR8] in [Garey and…
The degree of a CSP instance is the maximum number of times that any variable appears in the scopes of constraints. We consider the approximate counting problem for Boolean CSP with bounded-degree instances, for constraint languages…
Let gamma be a (not necessarily finite) structure with a finite relational signature. We prove that deciding whether a given existential positive sentence holds in gamma is in Logspace or complete for the class CSP(gamma)_NP under…
The so-called algebraic approach to the constraint satisfaction problem (CSP) has been a prevalent method of the study of complexity of these problems since early 2000's. The core of this approach is the notion of polymorphisms which…
We investigate the Constraint Satisfaction Problem (CSP) over templates with a group structure, and algorithms solving CSP that are equivariant, i.e. invariant under a natural group action induced by a template. Our main result is a method…
We study the computational complexity of exact minimisation of rational-valued discrete functions. Let $\Gamma$ be a set of rational-valued functions on a fixed finite domain; such a set is called a finite-valued constraint language. The…
We study the power of the bounded-width consistency algorithm in the context of the fixed-template Promise Constraint Satisfaction Problem (PCSP). Our main technical finding is that the template of every PCSP that is solvable in bounded…
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.
Neurosymbolic systems can satisfy logical constraints during learning without achieving the intended concept-label correspondence; this is a problem known as reasoning shortcuts. We formalize reasoning shortcuts as a constraint satisfaction…
This paper deals with the computational complexity of conditions which guarantee that the NP-hard problem of finding the sparsest solution to an underdetermined linear system can be solved by efficient algorithms. In the literature, several…
Here we study the computational complexity of the constrained synchronization problem for the class of regular commutative constraint languages. Utilizing a vector representation of regular commutative constraint languages, we give a full…
Valued constraint satisfaction problems (VCSPs) are discrete optimisation problems with a $(\mathbb{Q}\cup\{\infty\})$-valued objective function given as a sum of fixed-arity functions. In Boolean surjective VCSPs, variables take on labels…
An important question in the study of constraint satisfaction problems (CSP) is understanding how the graph or hypergraph describing the incidence structure of the constraints influences the complexity of the problem. For binary CSP…
We present a definition of the class NP in combinatorial context as the set of languages of structures defined by finitely many forbidden lifted substructures. We apply this to special syntactically defined subclasses and show how they…
Let $M$ be a real $r\times c$ matrix and let $k$ be a positive integer. In the column subset selection problem (CSSP), we need to minimize the quantity $\|M-SA\|$, where $A$ can be an arbitrary $k\times c$ matrix, and $S$ runs over all…
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. We show the close connection between this problem and a…
Finite valued constraint satisfaction problems are a formalism for describing many natural optimization problems, where constraints on the values that variables can take come with rational weights and the aim is to find an assignment of…
Functional constraints and bi-functional constraints are an important constraint class in Constraint Programming (CP) systems, in particular for Constraint Logic Programming (CLP) systems. CP systems with finite domain constraints usually…