summary by Olivier Dubois and Remi Monasson] The satisfaction of constrained formulae is a key issue in complexity theory. Many computational problems are shown to be NP-complete through a polynomial mapping onto the K-Satissability (SAT) problem. Recently, there has been much interest in a random version of the K-SAT problem deened as follows. Consider N Boolean variables x i , i = 1; : : :; N...

We study Random 2-SAT problem, in which 2-CNFs are sampled from a wide range of non-uniform distributions, including heavy-tailed using random model that is quite different the standard uniform 2-SAT. This SAT so-called configuration model, given by distribution ξ for degree (or number occurrences) each variable. To generate formula variable , generating several clones Then 2-clauses created ch...

The satisfiability (SAT) problem is a fundamental problem in mathematical logic, inference, automated reasoning, VLSI engineering, and computing theory. In this paper, following CNF and D N F local search methods, we introduce the Universal SAT problem model, UniSAT, which transforms the discrete SAT problem on Boolean space (0, l}"' into an unconstrained global optimization problem on real spa...

Prior algorithms known for exactly solving Max 2-Sat improve upon the trivial upper bound only for very sparse instances. We present new algorithms for exactly solving (in fact, counting) weighted Max 2-Sat instances. One of them has a good performance if the underlying constraint graph has a small separator decomposition, another has a slightly improved worst case performance. For a 2-Sat inst...

Zusammenfassung Abstract The Boolean conjunctive normal form (CNF) satisfiability problem, called SAT for short, gets as input a CNF formula and has to decide whether this formula admits a satisfying truth assignment. As is well known, the remarkable result by S. Cook in 1971 established SAT as the first and genuine complete problem for the complexity class NP [15]. Thus SAT resides at the hear...

consisting of a conjunction of clauses, where a clause is a disjunction of literals; a literal is either a variable v (a positive literal) or the negation of a variable ¬v (a negative literal). We are to decide if there is an assignment to the variables satisfying the formula, that is, an assignment under which every clause contains at least one true literal. The example formula is satisfied by...

consisting of a conjunction of clauses, where a clause is a disjunction of literals; a literal is either a variable v (a positive literal) or the negation of a variable ¬v (a negative literal). We are to decide if there is an assignment to the variables satisfying the formula, that is, an assignment under which every clause contains at least one true literal. The example formula is satisfied by...

The Boolean constraint satisfaction problem 3-SAT is arguably the canonical NP-complete problem. In contrast, 2-SAT can not only be decided in polynomial time, but in fact in deterministic linear time. In 2006, Bravyi proposed a physically motivated generalization of k-SAT to the quantum setting, defining the problem “quantum k-SAT”. He showed that quantum 2-SAT is also solvable in polynomial t...

conclusions according to the results, brucellosis has remained endemic in this region. most cases were detected by elisa igg. the highest kappa agreements were between tests krb-sat, krb-igg and ksat-igg, while the lowest levels of agreement were between tests sat-igm and elisa igm-igg. considering that elisa igm results are covered by sat and elisa igg test results, applications of this test d...

The Black-Box Hypothesis, introduced by Barak et al. [BGI12], states that any property of boolean functions decided efficiently (e.g., in BPP) with inputs represented by circuits can also be decided efficiently in the black-box setting, where an algorithm is given an oracle access to the input function and an upper bound on its circuit size. If this hypothesis is true, then P 6= NP. We focus on...