Satisfiability is one of the most popular NP-complete problems. There are two main types of algorithms for solving SAT, namely local search (for references see, for example, [3]) and DPLL-type (this type was first described in the work [5] of Davis and Putnam and [4] of Davis, Logemann and Loveland). A lot of effort has been invested in proving ”less-that-2N ” upper bounds for such algorithms. ...

Since the experimental paper of Cheeseman, Kanefsky and Taylor [1] phase transitions in combinatorial problems held the promise to shed light on the “practical” algorithmic complexity of combinatorial problems. However, the connection conjectured in [1] was easily seen to be inaccurate. A much more realistic possible connection has been highlighted by the results (based on experimental evidence...

One of the main reasons for the widespread use of SAT in many applications is that Conflict-Driven Clause Learning (CDCL) Boolean Satisfiability (SAT) solvers are so effective in practice. Since their inception in the mid-90s, CDCL SAT solvers have been applied, in many cases with remarkable success, to a number of practical applications. Examples of applications include hardware and software m...

We propose a new incomplete algorithm for the Maximum Satisfiability (MaxSAT) problem on unweighted Boolean formulas, focused specifically on instances for which proving unsatisfiability is already computationally difficult. For such instances, our approach is often able to identify a small number of what we call “bottleneck” constraints, in time comparable to the time it takes to prove unsatis...

We describe a new algorithm for solving linear integer programming problems. The algorithm performs a DPLL style search for a feasible assignment, while using a novel cut procedure to guide the search away from the conflicting states.

In this paper we introduce a new method for solving systems of linear inequalities. The algorithm incorporates many state-of-the-art techniques from DPLL-style reasoning. We prove soundness, completeness and termination of the method.

The area of Propositional Satisfiability (SAT) has been the subject of intensive research in recent years, with significant theoretical and practical contributions. From a practical perspective, a large number of very effective SAT solvers have recently been proposed, most of which based on improvements made to the original Davis-Putnam-Logemann-Loveland (DPLL) backtrack search SAT algorithm. T...

In this paper, we describe a new framework for evaluating Quantified Boolean Formulas (QBF). The new framework is based on the Davis-Putnam (DPLL) search algorithm. In existing DPLL based QBF algorithms, the problem database is represented in Conjunctive Normal Form (CNF) as a set of clauses, implications are generated from these clauses, and backtracking in the search tree is chronological. In...