Related papers: Certifying solution geometry in random CSPs: count…
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…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…
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…
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 distribution of overlaps of solutions of a random CSP is an indicator of the overall geometry of its solution space. For random $k$-SAT, nonrigorous methods from Statistical Physics support the validity of the ``one step replica…
Many AI synthesis problems such as planning or scheduling may be modelized as constraint satisfaction problems (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all…
Random constraint satisfaction problems (CSPs) have been widely studied both in AI and complexity theory. Empirically and theoretically, many random CSPs have been shown to exhibit a phase transition. As the ratio of constraints to…
We give a trichotomy theorem for the complexity of approximately counting the number of satisfying assignments of a Boolean CSP instance. Such problems are parameterised by a constraint language specifying the relations that may be used in…
The study of phase transition phenomenon of NP complete problems plays an important role in understanding the nature of hard problems. In this paper, we follow this line of research by considering the problem of counting solutions of…
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…
A constraint satisfaction problem (CSP) is a computational problem where the input consists of a finite set of variables and a finite set of constraints, and where the task is to decide whether there exists a satisfying assignment of values…
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)…
We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…
In this paper we study the solution space structure of model RB, a standard prototype of Constraint Satisfaction Problem (CSPs) with growing domains. Using rigorous the first and the second moment method, we show that in the solvable phase…
We define and study a statistical mechanics ensemble that characterizes connected solutions in constraint satisfaction problems (CSPs). Built around a well-known local entropy bias, it allows us to better identify hardness transitions in…
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…
We introduce tensor network contraction algorithms for counting satisfying assignments of constraint satisfaction problems (#CSPs). We represent each arbitrary #CSP formula as a tensor network, whose full contraction yields the number of…
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.…
Random constraint satisfaction problems (CSPs) are known to exhibit threshold phenomena: given a uniformly random instance of a CSP with $n$ variables and $m$ clauses, there is a value of $m = \Omega(n)$ beyond which the CSP will be…
We present an efficient algorithm to solve semirandom planted instances of any Boolean constraint satisfaction problem (CSP). The semirandom model is a hybrid between worst-case and average-case input models, where the input is generated by…