Related papers: Boolean PCSPs through the lens of Fourier Analysis
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…
This paper studies a class of probabilistic models on graphs, where edge variables depend on incident node variables through a fixed probability kernel. The class includes planted con- straint satisfaction problems (CSPs), as well as more…
The constraint satisfaction probem (CSP) is a well-acknowledged framework in which many combinatorial search problems can be naturally formulated. The CSP may be viewed as the problem of deciding the truth of a logical sentence consisting…
A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed…
We introduce a 2-round stochastic constraint-satisfaction problem, and show that its approximation version is complete for (the promise version of) the complexity class AM. This gives a `PCP characterization' of AM analogous to the PCP…
A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed…
In this paper, we study the problem of minimizing a polynomial function with literals over all binary points, often referred to as pseudo-Boolean optimization. We investigate the fundamental limits of computation for this problem by…
Neural networks excel across a wide range of tasks, yet remain black boxes. In particular, how their internal representations are shaped by the complexity of the input data and the problems they solve remains obscure. In this work, we…
Schaefer's dichotomy theorem [Schaefer, STOC'78] states that a boolean constraint satisfaction problem (CSP) is polynomial-time solvable if one of six given conditions holds for every type of constraint allowed in its instances. Otherwise,…
This paper studies complete $k$-Constraint Satisfaction Problems (CSPs), where an $n$-variable instance has exactly one nontrivial constraint for each subset of $k$ variables, i.e., it has $\binom{n}{k}$ constraints. A recent work started a…
Robust model fitting is a fundamental problem in computer vision: used to pre-process raw data in the presence of outliers. Maximisation of Consensus (MaxCon) is one of the most popular robust criteria and widely used. Recently (Tennakoon…
Polynomial threshold gates are basic processing units of an artificial neural network. When the input vectors are binary vectors, these gates correspond to Boolean functions and can be analyzed via their polynomial representations. In…
Schaefer's theorem is a complexity classification result for so-called Boolean constraint satisfaction problems: it states that every Boolean constraint satisfaction problem is either contained in one out of six classes and can be solved in…
Polynomial optimization encompasses a broad class of problems in which both the objective function and constraints are polynomial functions of the decision variables. In recent years, a substantial body of research has focused on…
We study sign structures of the ground states of spin-$1/2$ magnetic systems using the methods of Boolean Fourier analysis. Previously it was shown that the sign structures of frustrated systems are of complex nature: specifically, neural…
An important tool in the study of the complexity of Constraint Satisfaction Problems (CSPs) is the notion of a relational clone, which is the set of all relations expressible using primitive positive formulas over a particular set of base…
We determine the exact freezing threshold, r^f, for a family of models of random boolean constraint satisfaction problems, including NAE-SAT and hypergraph 2-colouring, when the constraint size is sufficiently large. If the…
Query evaluation over probabilistic databases is known to be intractable in many cases, even in data complexity, i.e., when the query is fixed. Although some restrictions of the queries [19] and instances [4] have been proposed to lower the…
The Constraint Satisfaction Problem (CSP) framework offers a simple and sound basis for representing and solving simple decision problems, without uncertainty. This paper is devoted to an extension of the CSP framework enabling us to deal…
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…