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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…
A classic result due to Schaefer (1978) classifies all constraint satisfaction problems (CSPs) over the Boolean domain as being either in $\mathsf{P}$ or $\mathsf{NP}$-hard. This paper considers a promise-problem variant of CSPs called…
Random $k$-SAT is the single most intensely studied example of a random constraint satisfaction problem. But despite substantial progress over the past decade, the threshold for the existence of satisfying assignments is not known precisely…
This paper describes a new approach on optimization of constraint satisfaction problems (CSPs) by means of substituting sub-CSPs with locally consistent regular membership constraints. The purpose of this approach is to reduce the number of…
Clustering is a well-known unsupervised machine learning approach capable of automatically grouping discrete sets of instances with similar characteristics. Constrained clustering is a semi-supervised extension to this process that can be…
The local behavior of typical solutions of random constraint satisfaction problems (CSP) describes many important phenomena including clustering thresholds, decay of correlations, and the behavior of message passing algorithms. When the…
Constraint satisfaction problems (or CSPs) have been extensively studied in, for instance, artificial intelligence, database theory, graph theory, and statistical physics. From a practical viewpoint, it is beneficial to approximately solve…
The quantified constraint satisfaction problem (QCSP) is a powerful framework for modelling computational problems. The general intractability of the QCSP has motivated the pursuit of restricted cases that avoid its maximal complexity. In…
We present a family of algorithms to solve random planted instances of any $k$-ary Boolean constraint satisfaction problem (CSP). A randomly planted instance of a Boolean CSP is generated by (1) choosing an arbitrary planted assignment…
A ternary permutation constraint satisfaction problem (CSP) is specified by a subset Pi of the symmetric group S_3. An instance of such a problem consists of a set of variables V and a set of constraints C, where each constraint is an…
The satisfiability threshold for constraint satisfaction problems is that value of the ratio of constraints (or clauses) to variables, above which the probability that a random instance of the problem has a solution is zero in the large…
We study interactions between Skolem Arithmetic and certain classes of Constraint Satisfaction Problems (CSPs). We revisit results of Glass er et al. in the context of CSPs and settle the major open question from that paper, finding a…
There has been great interest in identifying tractable subclasses of NP complete problems and designing efficient algorithms for these tractable classes. Constraint satisfaction and Bayesian network inference are two examples of such…
Constraint Satisfaction Problems are ubiquitous in fields ranging from the physics of solids to artificial intelligence. In many cases, such systems undergo a transition when the ratio of constraints to variables reaches some value…
We investigate the computational complexity of the problem of counting the maximal satisfying assignments of a Constraint Satisfaction Problem (CSP) over the Boolean domain {0,1}. A satisfying assignment is maximal if any new assignment…
For a finite relational structure A, let CSP(A) denote the CSP instances whose constraint relations are taken from A. The resulting family of problems CSP(A) has been considered heavily in a variety of computational contexts. In this…
We study the set of solutions of random k-satisfiability formulae through the cavity method. It is known that, for an interval of the clause-to-variables ratio, this decomposes into an exponential number of pure states (clusters). We refine…
The model of Dynamic Meta-Constraints has special activity constraints which can activate other constraints. It also has meta-constraints which range over other constraints. An algorithm is presented in which constraints can be assigned one…
In a broad class of sparse random constraint satisfaction problems(CSP), deep heuristics from statistical physics predict that there is a condensation phase transition before the satisfiability threshold, governed by one-step replica…
Given a constraint satisfaction problem (CSP) on $n$ variables, $x_1, x_2, \dots, x_n \in \{\pm 1\}$, and $m$ constraints, a global cardinality constraint has the form of $\sum_{i = 1}^{n} x_i = (1-2p)n$, where $p \in (\Omega(1), 1 -…