Related papers: The condensation phase transition in the regular $…
Corroborating a prediction from statistical physics, we prove that the Belief Propagation message passing algorithm approximates the partition function of the random $k$-SAT model well for all clause/variable densities and all inverse…
Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-rigorous statistical mechanics ideas have inspired a message passing algorithm called Belief Propagation Guided Decimation for finding satisfying…
We analyse the performance of Belief Propagation Guided Decimation, a physics-inspired message passing algorithm, on the random $k$-XORSAT problem. Specifically, we derive an explicit threshold up to which the algorithm succeeds with a…
The best current estimates of the thresholds for the existence of solutions in random constraint satisfaction problems ('CSPs') mostly derive from the first and the second moment method. Yet apart from a very few exceptional cases these…
Random constraint satisfaction problems play an important role in computer science and combinatorics. For example, they provide challenging benchmark instances for algorithms and they have been harnessed in probabilistic constructions of…
We show that throughout the satisfiable phase the normalised number of satisfying assignments of a random $2$-SAT formula converges in probability to an expression predicted by the cavity method from statistical physics. The proof is based…
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…
Survey propagation is a powerful technique from statistical physics that has been applied to solve the 3-SAT problem both in principle and in practice. We give, using only probability arguments, a common derivation of survey propagation,…
Message passing algorithms have proved surprisingly successful in solving hard constraint satisfaction problems on sparse random graphs. In such applications, variables are fixed sequentially to satisfy the constraints. Message passing is…
Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with…
The organization of high-dimensional probability spaces is a fundamental problem at the intersection of statistical physics and information theory. Here, we analyze the distributions populating level surfaces of the probability simplex…
The Survey Propagation (SP) algorithm for solving $k$-SAT problems has been shown recently as an instance of the Belief Propagation (BP) algorithm. In this paper, we show that for general constraint-satisfaction problems, SP may not be…
This paper provides a new conceptual perspective on survey propagation, which is an iterative algorithm recently introduced by the statistical physics community that is very effective in solving random k-SAT problems even with densities…
Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-constructive arguments show that F is satisfiable for clause/variable ratios m/n< r(k)~2^k ln 2 with high probability. Yet no efficient algorithm is…
In the last 30 years it was found that many combinatorial systems undergo phase transitions. One of the most important examples of these can be found among the random k-satisfiability problems (often referred to as k-SAT), asking whether…
Survey Propagation is an algorithm designed for solving typical instances of random constraint satisfiability problems. It has been successfully tested on random 3-SAT and random $G(n,\frac{c}{n})$ graph 3-coloring, in the hard region of…
We study the random K-satisfiability problem using a partition function where each solution is reweighted according to the number of variables that satisfy every clause. We apply belief propagation and the related cavity method to the…
In this paper we propose a new type of random CSP model, called Model RB, which is a revision to the standard Model B. It is proved that phase transitions from a region where almost all problems are satisfiable to a region where almost all…
Generating data from discrete distributions is important for a number of application domains including text, tabular data, and genomic data. Several groups have recently used random $k$-satisfiability ($k$-SAT) as a synthetic benchmark for…
We consider chains of random constraint satisfaction models that are spatially coupled across a finite window along the chain direction. We investigate their phase diagram at zero temperature using the survey propagation formalism and the…