Related papers: Comparing Beliefs, Surveys and Random Walks
We investigate how insights from statistical physics, namely survey propagation, can improve decoding of a particular class of sparse error correcting codes. We show that a recently proposed algorithm, time averaged belief propagation, is…
In this paper we present a backtracking version of the survey propagation algorithm. We show that the introduction of the simplest form of backtracking greatly improves the ability of the original survey propagation algorithm in solving…
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…
Partly on the basis of heuristic arguments from physics it has been suggested that the performance of certain types of algorithms on random $k$-SAT formulas is linked to phase transitions that affect the geometry of the set of satisfying…
I describe one quantum approach to solving 3-satisfiability (3-SAT), the well known problem in computer science. The approach is based on repeatedly measuring the truth value of the clauses forming the 3-SAT proposition using a…
To test incomplete search algorithms for constraint satisfaction problems such as 3-SAT, we need a source of hard, but satisfiable, benchmark instances. A simple way to do this is to choose a random truth assignment A, and then choose…
This paper presents an algorithm for 3-SAT problems. First, logical formulas are transformed into elementary algebraic formulas. Second, complex trigonometric functions are assigned to the variables in the elementary algebraic formulas, and…
When combined properly, search techniques can reveal the full potential of sophisticated branching heuristics. We demonstrate this observation on the well-known class of random 3-SAT formulae. First, a new branching heuristic is presented,…
Randomized algorithms for deciding satisfiability were shown to be effective in solving problems with thousands of variables. However, these algorithms are not complete. That is, they provide no guarantee that a satisfying assignment, if…
A solution to a 3-satisfiability (3-SAT) formula can be expanded into a cluster, all other solutions of which are reachable from this one through a sequence of single-spin flips. Some variables in the solution cluster are frozen to the same…
The ever-increasing number of nodes in current and future wireless communication networks brings unprecedented challenges for the allocation of the available communication resources. This is caused by the combinatorial nature of the…
We determine the complexity of several constraint satisfaction problems using the heuristic algorithm, WalkSAT. At large sizes N, the complexity increases exponentially with N in all cases. Perhaps surprisingly, out of all the models…
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…
The computational complexity of solving random 3-Satisfiability (3-SAT) problems is investigated. 3-SAT is a representative example of hard computational tasks; it consists in knowing whether a set of alpha N randomly drawn logical…
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…
3-SAT problem is of great importance to many technical and scientific applications. This paper presents a new hybrid evolutionary algorithm for solving this satisfiability problem. 3-SAT problem has the huge search space and hence it is…
Many difficult computational problems involve the simultaneous satisfaction of multiple constraints which are individually easy to satisfy. Such problems occur in diffractive imaging, protein folding, constrained optimization (e.g., spin…
This paper describes diff-SAT, an Answer Set and SAT solver which combines regular solving with the capability to use probabilistic clauses, facts and rules, and to sample an optimal world-view (multiset of satisfying Boolean variable…
The structural phase transitions and computational complexity of random 3-SAT instances are traditionally described using thermodynamic analogies from statistical physics, such as Replica Symmetry Breaking and energy landscapes. While…
If the three dimensional self-avoiding walk (SAW) is conformally invariant, then one can compute the hitting densities for the SAW in a half-space and in a sphere. The ensembles of SAW's used to define these hitting densities involve walks…