Programs for the Boolean satisfiability problem (SAT), i.e., SAT solvers, are nowadays used as core decision procedures for a wide range of combinatorial problems. Advances in SAT solving during the last 10–15 years have been spurred by yearly solver competitions. In this article, we report on the main SAT solver competition held in 2012, SAT Challenge 2012. Besides providing an overview of how...

The propositional satisfiability (SAT) problem is one of the most fundamental problems in computer science. SAT solvers have been successfully applied to a wide range of practical applications, including hardware model checking, software model finding, equivalence checking, and planning, among many others. Empirical research has been very fruitful for the development of efficient methods for SA...

Boolean SATisfiability (SAT) is an important problem in AI. SAT solvers have been effectively used in important industrial applications including automated planning and verification. In this paper, we present novel algorithms for fast SAT solving by employing two common subclause elimination (CSE) approaches. Our motivation is that modern SAT solving techniques can be more efficient on CSE-proc...

Exact Max-SAT solvers, compared with SAT solvers, apply little inference at each node of the proof tree. Commonly used SAT inference rules like unit propagation produce a simplified formula that preserves satisfiability but, unfortunately, solving the Max-SAT problem for the simplified formula is not equivalent to solving it for the original formula. In this paper, we define a number of origina...

The success of portfolio approaches in SAT solving relies on the observation that different SAT solvers may dramatically change their performance depending on the class of SAT instances they are trying to solve. In these approaches, a set of features of the problem is used to build a prediction model, which classifies instances into classes, and computes the fastest algorithm to solve each of t...

For a fixed graph H, a graph G is H-saturated if there is no copy of H in G, but for any edge e 6∈ G, there is a copy of H in G + e. The collection of Hsaturated graphs of order n is denoted by SAT(n,H), and the saturation number, sat(n,H), is the minimum number of edges in a graph in SAT(n,H). Let Tk be a tree on k vertices. The saturation numbers sat(n, Tk) for some families of trees will be ...

In recent years there has been signi1cant interest in the study of random k-SAT formulae. For a given set of n Boolean variables, let Bk denote the set of all possible disjunctions of k distinct, non-complementary literals from its variables (k-clauses). A random k-SAT formula Fk(n; m) is formed by selecting uniformly and independently m clauses from Bk and taking their conjunction. Motivated b...

The study was designed to investigate the cellular mechanisms underlying the differential fat expansion in different fat depots in wild type (WT) and ob/ob (OB) mice. At 6 weeks old, no differences in fat mass were found between SAT and VAT in WT mice, while O-SAT showed significantly higher weight than that of O-VAT. The average adipocyte size of SAT (~ 4133.47 μm2) was smaller than that of VA...