Introduced here is a novel application of Satisfiability (SAT) to the set membership problem with specific focus on efficiently testing whether large sets contain a given element. Such tests can be greatly enhanced via the use of filters, probabilistic algorithms that can quickly decide whether or not a given element is in a given set. This article proposes SAT filters (i.e., filters based on S...

In recent years, portfolio approaches to solving SAT problems and CSPs have become increasingly common. There are also a number of di erent encodings for representing CSPs as SAT instances. In this paper, we leverage advances in both SAT and CSP solving to present a novel hierarchical portfolio-based approach to CSP solving, which we call Proteus, that does not rely purely on CSP solvers. Inste...

Bollobás, Brightwell and Leader [2] showed that there are at most 2( n 2)+o(n 2) 2-SAT functions on n variables, and conjectured that in fact almost every 2-SAT function is unate: i.e., has a 2-SAT formula in which no variable’s positive and negative literals both appear. We prove their conjecture, finding the number of 2-SAT functions on n variables to be 2( n 2)+n(1 + o(1)). As a corollary of...

This paper proposes a stochastic, and complete, backtrack search algorithm for Propositional Satisfiability (SAT). In recent years, randomization has become pervasive in SAT algorithms. Incomplete algorithms for SAT, for example the ones based on local search, often resort to randomization. Complete algorithms also resort to randomization. These include, state-of-the-art backtrack search SAT al...

We are dealing with solving difficult SAT instances in this paper. We propose a method for preprocessing SAT instances (CNF formulas) by using consistency techniques known from constraint programming methodology and by using our own consistency technique based on clique decomposition of a graph representing conflicts in the input formula. The clique decomposition allows us to make a strong reas...

Maximum satisfiability (Max-SAT) is more general and more difficult to solve than satisfiability (SAT). In this paper, we first investigate the effectiveness of Walksat, one of the best local search algorithms designed for SAT, on Max-SAT. We show that Walksat is also effective on Max-SAT, while its effectiveness degrades as the problem is more constrained. We then develop a novel method that e...

One of the most successful approaches to automated planning is the translation to propositional satis ability (SAT). This thesis evaluates incremental SAT solving for several modern encodings for SAT based planning. Experiments based on benchmarks from the 2014 International Planning Competition show that an incremental approach signi cantly outperforms non-incremental solving. Although, planni...

Twelve years ago, Brian Powell and Lala Carr Steelman analyzed state SAT scores in a landmark article in the Harvard Educational Review. At the time, politicians and the media, among others, had been using raw state SAT scores to make inferences about the relative quality of education among the U.S. states. Powell and Steelman, however, found that more than 80 percent of the variation in averag...

Karloo and Zwick obtained recently an optimal 7=8-approximation algorithm for MAX 3-SAT. In an attempt to see whether similar methods can be used to obtain a 7=8-approximation algorithm for MAX SAT, we consider the most natural generalization of MAX 3-SAT, namely MAX 4-SAT. We present a semideenite programming relaxation of MAX 4-SAT and a new family of rounding procedures that try to cope well...

Since the slowing of the trend of increasing surface air temperature (SAT) in the late 1990 s, intense interest and debate have arisen concerning the contribution of human activities to the warming observed in previous decades. Although several explanations have been proposed for the warming-trend slowdown (WTS), none has been generally accepted. We investigate the WTS using a recently develope...