We present a new deterministic algorithm for the #3-SAT problem, based on the DPLL strategy. It uses a new approach for counting models of instances with low density. This allows us to assume the adding of more 2-clauses than in previous algorithms. The algorithm achieves a running time of O(1.6423) in the worst case which improves the current best bound of O(1.6737) by Dahllöf et al.

Execution of most of the modern DPLL-based SAT solvers is guided by a number of heuristics. Decisions made during the search process are usually driven by some fixed heuristic policies. Despite the outstanding progress in SAT solving in recent years, there is still an appealing lack of techniques for selecting policies appropriate for solving specific input formulae. In this paper we present a ...

The past few years have seen enormous progress in the performance of propositional satisfiability (SAT) solvers, and consequently SAT solvers are widely used in industry for many applications. In spite of this progress, there is strong demand for higher SAT algorithms efficiency to solve harder and larger problems. Unfortunately, most modern solvers are sequential and fewer are parallel. Our in...

Bayesian inference is an important problem with numerous applications in probabilistic reasoning. Counting satisfying assignments is a closely related problem of fundamental theoretical importance. In this paper, we show that plain old DPLL equipped with memoization (an algorithm we call #DPLLCache) can solve both of these problems with time complexity that is at least as good as state-of-the-a...

We investigate quantum backtracking algorithms of a type previously introduced by Montanaro (arXiv:1509.02374). These algorithms explore trees of unknown structure, and in certain cases exponentially outperform classical procedures (such as DPLL). Some of the previous work focused on obtaining a quantum advantage for trees in which a unique marked vertex is promised to exist. We remove this res...

This paper describes the integration of an LP solver into iSAT, a Satisfiability Modulo Theories solver that can solve Boolean combinations of linear and nonlinear constraints. iSAT is a tight integration of the well-known DPLL algorithm and interval constraint propagation allowing it to reason about linear and nonlinear constraints. As interval arithmetic is known to be less efficient on solvi...

Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over linear integer or real arithmetic, or other theories. In this survey, we explain the combination of propositional satisfiability and decision procedures for conjunctions known as DPLL(T), and the alternative “natural domain” approaches. We also cover quantifiers, Craig interpolants, polynomial...

We present a novel expansion based decision procedure for quantified boolean formulas (QBF) in conjunctive normal form (CNF). The basic idea is to resolve existentially quantified variables and eliminate universal variables by expansion. This process is continued until the formula becomes propositional and can be solved by any SAT solver. On structured problems our implementation quantor is com...

Look-ahead SAT solvers are the most suitable to solve random k-SAT formulas. Based on the DPLL framework, they use branching heuristics. We generalise the application of the efficient recursive weight heuristic for k-SAT problems. The heuristic and an efficient implementation are presented in this paper. Parameter tuning is performed providing experimental results. Further experiments demonstra...