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The constraint satisfaction problem (CSP) has important applications in computer science and AI. In particular, infinite-domain CSPs have been intensively used in subareas of AI such as spatio-temporal reasoning. Since constraint…
This paper draws on diverse areas of computer science to develop a unified view of computation: (1) Optimization in operations research, where a numerical objective function is maximized under constraints, is generalized from the numerical…
Continuous search problems (CSPs), which involve finding solutions within a continuous domain, frequently arise in fields such as optimization, physics, and engineering. Unlike discrete search problems, CSPs require navigating an…
Constraint satisfaction problems (CSPs) consist of a set of variables taking values from some finite domain and a set of local constraints on these variables. The objective is to find an assignment to the variables that maximizes the…
The containment problem of Datalog queries is well known to be undecidable. There are, however, several Datalog fragments for which containment is known to be decidable, most notably monadic Datalog and several "regular" query languages on…
The Constraint-satisfaction problem (CSP) is fundamental in mathematics, physics, and theoretical computer science. Continuous local search (CLS) solvers, as recent advancements, can achieve highly competitive results on certain classes of…
We build on a recently proposed method for explaining solutions of constraint satisfaction problems. An explanation here is a sequence of simple inference steps, where the simplicity of an inference step is measured by the number and types…
A constraint satisfaction problem (CSP) is a problem of computing a homomorphism ${\bf R} \rightarrow {\bf \Gamma}$ between two relational structures. Analyzing its complexity has been a very fruitful research direction, especially for…
Testing containment of queries is a fundamental reasoning task in knowledge representation. We study here the containment problem for Conjunctive Regular Path Queries (CRPQs), a navigational query language extensively used in ontology and…
In this paper we study the complexity of counting Constraint Satisfaction Problems (CSPs) of the form #CSP($\mathcal{C}$,-), in which the goal is, given a relational structure $\mathbf{A}$ from a class $\mathcal{C}$ of structures and an…
We study the optimization version of constraint satisfaction problems (Max-CSPs) in the framework of parameterized complexity; the goal is to compute the maximum fraction of constraints that can be satisfied simultaneously. In standard…
Reverse engineering problems for conjunctive queries (CQs), such as query by example (QBE) or definability, take a set of user examples and convert them into an explanatory CQ. Despite their importance, the complexity of these problems is…
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…
Semidefinite programs (SDPs) often arise in relaxations of some NP-hard problems, and if the solution of the SDP obeys certain rank constraints, the relaxation will be tight. Decomposition methods based on chordal sparsity have already been…
An active topic in the study of random constraint satisfaction problems (CSPs) is the geometry of the space of satisfying or almost satisfying assignments as the function of the density, for which a precise landscape of predictions has been…
In this paper we systematically investigate the connections between logics with a finite number of variables, structures of bounded pathwidth, and linear Datalog Programs. We prove that, in the context of Constraint Satisfaction Problems,…
A subset of Q^n is called semilinear (or piecewise linear) if it is Boolean combination of linear half-spaces. We study the computational complexity of the constraint satisfaction problem (CSP) over the rationals when all the constraints…
Many fundamental problems in artificial intelligence, knowledge representation, and verification involve reasoning about sets and relations between sets and can be modeled as set constraint satisfaction problems (set CSPs). Such problems…
The constraint satisfaction problem (CSP) on a finite relational structure B is to decide, given a set of constraints on variables where the relations come from B, whether or not there is a assignment to the variables satisfying all of the…
CSP sparsification, introduced by Kogan and Krauthgamer (ITCS 2015), considers the following question: how much can an instance of a constraint satisfaction problem be sparsified (by retaining a reweighted subset of the constraints) while…