Ohya and Volovich have been proposed a new quantum computation model with chaos amplification to solve the SAT problem, which went beyond usual quantum algorithm. In this paper we study the complexity of the SAT algorithm by counting the steps of computation algorithm rigorously, which was mentioned in the paper [1, 2, 3, 5, 7]. For this purpose, we refine the quantum gates treating the SAT pro...

The diagnosis of a discrete-event system is the problem of computing possible behaviors of the system given observations of the actual behavior, and testing whether the behaviors are normal or faulty. We show how the diagnosis problems can be translated into the propositional satisfiability problem (SAT) and solved by algorithms for SAT. Our experiments demonstrate that current SAT algorithms c...

Propositional satisfiability (SAT) is the archetypal NP-complete problem [1]. A great deal of recent SAT research, particularly on the performance of SAT solvers, has been driven by structured instances, which are obtained by mapping another problem class into SAT. It is possible to efficiently solve a wide range of problems by mapping them into SAT and solving the SAT representation of the pro...

We propose a variable ordering heuristic for SAT, which is based on a structural analysis of the SAT problem. We show that when the heuristic is used by a Davis-Putnam SAT solver that employs conflict-directed backtracking, it produces a divide-and-conquer behavior in which the SAT problem is recursively decomposed into smaller problems that are solved independently. We discuss the implications...

Witold Pedrycz, Giancarlo Succi, and Ofer Shai Owing to the immense size of the search space in the SAT problem, evolutionary computing arises as a viable and attractive option. The objective of this study is to formulate the SAT problem in the evolutionary setting and carry out comprehensive xperimental studies. The approach relies on the embedding principle: we generalize the Boolean problem ...

The Boolean constraint satisfaction problem 3-SAT is arguably the canonical NP-complete problem. In contrast, 2-SAT can not only be decided in polynomial time, but in fact in deterministic linear time. In 2006, Bravyi proposed a physically motivated generalization of k-SAT to the quantum setting, defining the problem “quantum k-SAT”. He showed that quantum 2-SAT is also solvable in polynomial t...

We consider the problem of generating hard instances for the Satisfying Assignment Search Problem (in short, SAT). It is not known whether SAT is difficult on average, while it has been believed that the Factorization Problem (in short, FACT) is hard on average. Thus, one can expect to generate hard-on-average instances by using a reduction from FACT to SAT. Although the asymptotically best red...

We introduce h-modularity, a structural parameter of CNF formulas, and present algorithms that render the decision problem SAT and the model counting problem #SAT fixed-parameter tractable when parameterized by h-modularity. The new parameter is defined in terms of a partition of clauses of the given CNF formula into strongly interconnected communities which are sparsely interconnected with eac...

In today’s lecture, we will construct exponential sized PCPs for NP. More formally, we will show that the NP-Complete problem, Circuit-Satisfiability (Circuit-SAT) is in PCP1,1−δ[O(n), O(1)] for some 0 < δ < 1. Recall that the PCP Theorem states that Circuit-SAT ∈ PCP1,1−δ[O(log n), O(1)]. However, as we will see in later lectures, the exponential sized PCPs for Circuit-SAT will be used in prov...

UNIQUE SAT is the problem of deciding whether a given Boolean formula has exactly one satisfying truth assignment. This problem is a typical (moreover complete) representative of a natural class of problems about unique solutions. All these problems belong to the class DIFe= {L1--L2:L1,Lz~NP} studied by Papadimitriou and Yannakakis. We consider the relationship between these two classes, partic...