Boolean satisfiability (SAT) is a core non polynomial (NP)-complete problem. Several heuristic software and hardware approaches have been proposed to solve this problem. The authors present a hardware solution to the SATproblem.They propose a custom integrated circuit (IC) to implement their approach, in which the traversal of the implication graph as well as conflict clause generation are perf...

Several combinatorial optimization problems can be translated into the Weighted Partial Maximum Satisfiability (WPMS) problem. This is an optimization variant of the Satisfiability (SAT) problem. There are two main families of WPMS solvers based on SAT technology: branch and bound and SAT-based. From the MaxSAT evaluations, we have learned that SAT-based solvers dominate on industrial instances...

The paper shows that the data exchange between a host computer and FPGA-based matrix-oriented accelerators for solving the SAT problem might influence the total time of computations significantly. Two methods based on data compression have been examined. The first one provides matrix compression in a host computer and decompression in an FPGA. It is shown that although some improvements have be...

Model counting is the task of computing the number of assignments to variables V that satisfy a given propositional theory F . The model counting problem is denoted as #SAT. Model counting is an essential tool in probabilistic reasoning. In this paper, we introduce the problem of model counting projected on a subset of original variables that we call priority variables P ⊆ V. The task is to com...

Bounded Model Checking based on SAT methods has recently been introduced as a complementary technique to BDD-based Symbolic Model Checking. The basic idea is to search for a counter example in executions whose length is bounded by some integer k. The BMC problem can be eeciently reduced to a propositional satissabil-ity problem, and can therefore be solved by SAT methods rather than BDDs. SAT p...

The satisfiability (SAT) problem is a central problem in mathematical logic, computing theory, and artificial intelligence. An instance of SAT is specified by a set of boolean variables and a propositional formula in conjunctive normal form. Given such an instance, the SAT problem asks whether there is a truth assignment to the variables such that the formula is satisfied. It is well known that...

The satisfiability problem is a basic core NP-complete problem. In recent years, a lot of heuristic algorithms have been developed to solve this problem, and many experiments have evaluated and compared the performance of different heuristic algorithms. However, rigorous theoretical analysis and comparison are rare. This paper analyzes and compares the expected runtime of three basic heuristic ...

Model counting is the task of computing the number of assignments to variables V that satisfy a given propositional theory F . The model counting problem is denoted as #SAT. Model counting is an essential tool in probabilistic reasoning. In this paper, we introduce the problem of model counting projected on a subset of original variables that we call priority variables P ⊆ V. The task is to com...

We provide some evidence that Unique k-SAT is as hard to solve as general k-SAT, where k-SAT denotes the satisfiability problem for k-CNFs with at most k literals in each clause and Unique k-SAT is the promise version where the given formula has 0 or 1 solutions. Namely, defining for each k > 1, sk = inf{δ > 0 | ∃ a O(2)-time randomized algorithm for k-SAT} and, similarly, σk = inf{δ > 0 | ∃ a ...

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...