We introduce a greedy local search procedure called GSAT for solving propositional satisfiability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approaches such as the Davis-Putnam procedure or resolution. We also show that GSAT can solve structured satisfiability problems quickly. In particular, we solve encodings of graph coloring problems, N-queens, and Boolean induction. General application strategies and limitations of the approach are also discussed. GSAT is best viewed as a model-finding procedure. Its good performance suggests that it may be advantageous to reformulate reasoning tasks that have traditionally been viewed as theorem-proving problems as model-finding tasks.

It has recently been shown that local search is surprisingly good at finding satisfying assignments for certain classes of CNF formulas [24]. In this paper we demonstrate that the power of local search for satisfiability testing can be further enhanced by employinga new strategy, called "mixed random walk", for escaping from local minima. We present experimental results showing how this strategy allows us to handle formulas that are substantially larger than those that can be solved with basic local search. We also present a detailed comparison of our random walk strategy with simulated annealing. Our results show that mixed random walk is the superior strategy on several classes of computationally difficult problem instances. Finally, we present results demonstrating the effectiveness of local search with walk for solving circuit synthesis and diagnosis problems.

GSAT is a randomized local search procedure for solving propositional satisfiability problems (Selman et al. 1992). GSAT can solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approaches such as the Davis-Putnam procedure. GSAT also efficiently solves encodings of graph coloring problems, N-queens, and Boolean induction. However, GSAT does not perform as well on handcrafted encodings of blocks-world planning problems and formulas with a high degree of asymmetry. We present three strategies that dramatically improve GSAT's performance on such formulas. These strategies, in effect, manage to uncover hidden structure in the formula under considerations, thereby significantly extending the applicability of the GSAT algorithm.

... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400-variable 3-SAT problems in about 2 hours on the average. In general, it can solve hard n-variable random 3-SAT problems with search trees of size O(2 n=18:7 ). In addition to justifying these claims, this dissertation describes the most significant achievements of other researchers in this area, and discusses all of the widely known general techniques for speeding up SAT search algorithms. It should be useful to anyone interested in NP-complete problems or combinatorial optimization in general, and it should be particularly useful to researchers in either Artificial Intelligence or Operations Research.

. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computer-aided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...

Abstract. We discuss fast exponential time solutions for NP-complete problems. We survey known results and approaches, we provide pointers to the literature, and we discuss several open problems in this area. The list of discussed NP-complete problems includes the travelling salesman problem, scheduling under precedence constraints, satisfiability, knapsack, graph coloring, independent sets in graphs, bandwidth of a graph, and many more. 1

We define and analyze quantum computational variants of random walks on one-dimensional lattices. In particular, we analyze a quantum analog of the symmetric random walk, which we call the Hadamard walk. Several striking differences between the quantum and classical cases are observed. For example, when unrestricted in either direction, the Hadamard walk has position that is nearly uniformly distributed in the range [\Gamma t= p

Stochastic local search (SLS) algorithms for the propositional satisfiability problem (SAT) have been successfully applied to solve suitably encoded search problems from various domains. One drawback of these algorithms is that they are usually incomplete. We refine the notion of incompleteness for stochastic decision algorithms by introducing the notion of "probabilistic asymptotic completeness" (PAC) and prove for a number of well-known SLS algorithms whether or not they have this property. We also give evidence for the practical impact of the PAC property and show how to achieve the PAC property and significantly improved performance in practice for some of the most powerful SLS algorithms for SAT, using a simple and general technique called "random walk extension".

We develop a model-based approach to reasoning, in which the knowledge base is represented as a set of models (satisfying assignments) rather than a logical formula, and the set of queries is restricted. We show that for every propositional knowledge base (KB) there exists a set of characteristic models with the property that a query is true in KB if and only if it is satisfied by the models in this set. We characterize a set of functions for which the model-based representation is compact and provides efficient reasoning. These include cases where the formula-based representation does not support efficient reasoning. In addition, we consider the model-based approach to abductive reasoning and show that for any propositional KB, reasoning with its model-based representation yields an abductive explanation in time that is polynomial in its size. Some of our technical results make use of the Monotone Theory, a new characterization of Boolean functions recently introduced. The notion of ...

We introduce a technique for analyzing the behavior of sophisticated A.I. search programs working on realistic, large-scale problems. This approach allows us to predict where, in a space of problem instances, the hardest problems are to be found and where the fluctuations in difficulty are greatest. Our key insight is to shift emphasis from modelling sophisticated algorithms directly to modelling a search space that captures their principal effects. We compare our model’s predictions with actual data on real problems obtained independently and show that the agreement is quite good. By systematically relaxing our underlying modelling assumptions we identify their relative contribution to the remaining error and then remedy it. We also discuss further applications of our model and suggest how this type of analysis can be generalized to other kinds of A.I. problems. Chapter 1