Related papers: From one solution of a 3-satisfiability formula to…
Random $K$-satisfiability ($K$-SAT) is a paradigmatic model system for studying phase transitions in constraint satisfaction problems and for developing empirical algorithms. The statistical properties of the random $K$-SAT solution space…
Three algorithms are presented that determine the existence of satisfying assignments for 3SAT Boolean satisfiability expressions. One algorithm is presented for determining an instance of a satisfying assignment, where such exists. The…
We study a random system of $cn$ linear equations over $n$ variables in GF(2), where each equation contains exactly $r$ variables; this is equivalent to $r$-XORSAT. \cite{ikkm,amxor} determined the clustering threshold, $c^*_r$: if…
The local search algorithm WSat is one of the most successful algorithms for solving the satisfiability (SAT) problem. It is notably effective at solving hard Random 3-SAT instances near the so-called `satisfiability threshold', but still…
We consider the problem of solving floating-point constraints obtained from software verification. We present UppSAT --- a new implementation of a systematic approximation refinement framework [ZWR17] as an abstract SMT solver. Provided…
Clustering provides a common means of identifying structure in complex data, and there is renewed interest in clustering as a tool for the analysis of large data sets in many fields. A natural question is how many clusters are appropriate…
We present a procedure to solve the inverse Ising problem, that is to find the interactions between a set of binary variables from the measure of their equilibrium correlations. The method consists in constructing and selecting specific…
The computational cost of counting the number of solutions satisfying a Boolean formula, which is a problem instance of #SAT, has proven subtle to quantify. Even when finding individual satisfying solutions is computationally easy (e.g.…
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…
Boolean satisfiability (SAT) is a propositional logic problem of determining whether an assignment of variables satisfies a Boolean formula. Many combinatorial optimization problems can be formulated in Boolean SAT logic -- either as k-SAT…
Several fragments of the satisfiability problem have been studied in the literature. Among these, Linear 3-SAT is a satisfaction problem in which each clause (viewed as a set of literals) intersects with at most one other clause; moreover,…
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…
Reduction of frustration was the driving force in an approach to social balance as it was recently considered by Antal \emph{et al.} [ T. Antal, P. L. Krapivsky, and S. Redner, Phys. Rev. E {\bf 72}, 036121 (2005). ]. We generalize their…
We introduce the aggregated clustering problem, where one is given $T$ instances of a center-based clustering task over the same $n$ points, but under different metrics. The goal is to open $k$ centers to minimize an aggregate of the…
We investigate geometrical properties of the random K-satisfiability problem using the notion of x-satisfiability: a formula is x-satisfiable if there exist two SAT assignments differing in Nx variables. We show the existence of a sharp…
Many community detection algorithms are inherently stochastic, leading to variations in their output depending on input parameters and random seeds. This variability makes the results of a single run of these algorithms less reliable.…
We study a simple and exactly solvable model for the generation of random satisfiability problems. These consist of $\gamma N$ random boolean constraints which are to be satisfied simultaneously by $N$ logical variables. In…
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…
In probabilistic logic entailments, even moderate size problems can yield linear constraint systems with so many variables that exact methods are impractical. This difficulty can be remedied in many cases of interest by introducing a three…
We study the performances of stochastic heuristic search algorithms on Uniquely Extendible Constraint Satisfaction Problems with random inputs. We show that, for any heuristic preserving the Poissonian nature of the underlying instance, the…