In this paper we provide SAT-solving procedures that use the idea of decomposition together with the heuristic of solving the most constrained subproblem first. We present two approaches. We provide an algorithm to find the most constrained subproblem of a propositional SAT problem in polynomial time. We use this algorithm iteratively to decompose a SAT problem into partitions. We also provide ...

We study how propositional satissability (SAT) problems can be reformulated as constraint satisfaction problems (CSPs). We analyse four diierent mappings of SAT problems into CSPs. For each mapping , we compare theoretically the performance of systematic algorithms like FC and MAC applied to the encoding against the Davis-Putnam procedure applied to the original SAT problem. We also compare loc...

In this paper we study the problem of estimating the time required to process decompositions of hard SAT instances encoding inversion problems of some cryptographic functions. In particular, we consider one type of SAT decompositions, usually referred to as SAT partitioning. The effectiveness of a specific SAT parititioning is the total time required to solve all SAT instances from this partiti...

Like simpler graphs, nested (hypernodal) graphs consist of two components: a set of nodes and a set of edges, where each edge connects a pair of nodes. In the hypernodal graph model, however, a node may contain other graphs [1]; so that a node may be contained in a graph that it contains. The inherently recursive structure of the hypernodal graph model aptly characterizes both the structure and...

In this paper, stickers are used to construct a solution space of DNA for the satisfiability (SAT) problem. Simultaneously DNA operations are applied in the sticker-based model to develop a DNA algorithm. The result of the proposed algorithm shows that the SAT problem is resolved with biological operation in the sticker-based model for solution space of sticker. Furthermore, this work presents ...

This paper focuses on finding optimal solutions to the multiagent path finding (MAPF) problem over undirected graphs where the task is to find non-colliding paths for multiple agents, each with a different start and goal position. An encoding of MAPF to Boolean satisfiability (SAT) is already known to the makespan optimal variant of the problem. In this paper we present the first SAT-solver for...

The Boolean Satisfiability (SAT) decision problem can be deservedly declared a success story of computer science. Although SAT was the first problem to be proved NP-complete, the last decade and a half have seen dramatic improvements in the performance of SAT solvers on many practical problem instances. These performance improvements enabled a wide range of real-world applications, several of w...

Complexity of a quantum analogue of the satisfiability problem is studied. Quantum k-SAT is a problem of verifying whether there exists a state |Ψ〉 of n qubits such that its k-qubit reduced density matrices have support on prescribed subspaces. We present a classical algorithm solving quantum 2-SAT in a polynomial time. It generalizes the well-known algorithm for the classical 2-SAT. Besides, w...

The Boolean Satisfiability Problem (SAT) belongs to the class of NP-complete problems, meaning that there is no known deterministic algorithm that can solve an arbitrary problem instance in less than exponential time (parametrized on the length of the input). There is great industrial demand for solving SAT, motivating the need for algorithms which perform well. I present a comparison of two ap...

The quantified boolean formula (QBF) problem is a powerful generalization of the boolean satisfiability (SAT) problem where variables can be both universally and existentially quantified. Inspired by the fruitfulness of the established model for generating random SAT instances, we define and study a general model for generating random QBF instances. We exhibit experimental results showing that ...