has seen much interest in not just the theoretical computer science community, but also in areas where practical solutions to this problem enable significant practical applications. Since the first development of the basic search based algorithm proposed by Davis, Putnam, Logemann and Loveland (DPLL) about forty years ago, this area has seen active research effort with many interesting contributions that have culminated in state-of-the-art SAT solvers today being able to handle problem instances with thousands, and in same cases even millions, of variables. In this paper we examine some of the main ideas along this passage that have led to our current capabilities. Given the depth of the literature in this field, it is impossible to do this in any comprehensive way; rather we focus on techniques with consistent demonstrated efficiency in available solvers. For the most part, we focus on techniques within the basic DPLL search framework, but also briefly describe other approaches and look at some possible future research directions. 1.

. 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...

We compare SAT-checkers and decision diagrams on the evaluation of Boolean formulas produced in the formal verification of both correct and buggy versions of superscalar and VLIW microprocessors. We identify one SAT-checker that significantly outperforms the rest. We evaluate ways to enhance its performance by variations in the generation of the Boolean correctness formulas. We reassess optimizations previously used to speed up the formal verification and probe future challenges.

The hybridisation of systematic and stochastic search is an active research area with potential bene ts for real-world combinatorial problems. This paper shows that randomising the backtracking component of a systematic backtracker can improve its scalability to equal that of stochastic local search. The hybrid may be viewed as stochastic local search in a constrained space, cleanly combining local search with constraint programming techniques. The approach is applied to two very dierent problems. Firstly a hybrid of local search and constraint propagation is applied to hard random 3-SAT problems, and is the rst constructive search algorithm to solve very large instances. Secondly a hybrid of local search and branch-and-bound is applied to low-autocorrelation binary sequences (a notoriously dicult communications engineering problem), and is the rst stochastic search algorithm to nd optimal solutions. These results show that the approach is a promising one for both constraint satisfaction and optimisation problems.

Abstract. In this paper, we show how Guided Local Search (GLS) can be applied to the SAT problem and show how the resulting algorithm can be naturally extended to solve the weighted MAX-SAT problem. GLS is a general, penalty-based metaheuristic, which sits on top of local search algorithms to help guide them out of local minima. GLS has been shown to be successful in solving a number of practical real life problems, such as the travelling salesman problem, BT's workforce scheduling problem, the radio link frequency assignment problem and the vehicle routing problem. We present empirical results of applying GLS to instances of the SAT problem from the DIMACS archive and also a small set of weighted MAX-SAT problem instances and compare them against the results of other local search algorithms for the SAT problem. Keywords: SAT problem, Local Search, Meta-heuristics, Optimisation 1.

Boolean Satisfiability (SAT) is often used as the underlying model for a significant and increasing number of applications in Electronic Design Automation (EDA) as well as in many other fields of Computer Science and Engineering. In recent years, new and efficient algorithms for SAT have been developed, allowing much larger problem instances to be solved. SAT “packages” are currently expected to have an impact on EDA applications similar to that of BDD packages since their introduction more than a decade ago. This tutorial paper is aimed at introducing the EDA professional to the Boolean satisfiability problem. Specifically, we highlight the use of SAT models to formulate a number of EDA problems in such diverse areas as test pattern generation, circuit delay computation, logic optimization, combinational equivalence checking, bounded model checking and functional test vector generation, among others. In addition, we provide an overview of the algorithmic techniques commonly used for solving SAT, including those that have seen widespread use in specific EDA applications. We categorize these algorithmic techniques, indicating which have been shown to be best suited for which tasks.

SAT Competition 2002 held in March--May 2002 in conjunction with SAT 2002 (the Fifth International Symposium on the Theory and Applications of Satisfiability Testing). About 30 solvers and 2300 benchmarks took part in the competition, which required more than 2 CPU years to complete the evaluation. In this report

Algorithms based on following local gradient information are surprisingly effective for certain classes of constraint satisfaction problems. Unfortunately, previous local search algorithms are notoriously incomplete: They are not guaranteed to find a feasible solution if one exists and they cannot be used to determine unsatisfiability. We present an algorithmic framework for complete local search and discuss in detail an instantiation for the propositional satisfiability problem (SAT). The fundamental idea is to use constraint learning in combination with a novel objective function that converges during search to a surface without local minima. Although the algorithm has worst-case exponential space complexity, we present empirical results on challenging SAT competition benchmarks that suggest that our implementation can perform as well as state-of-the-art solvers based on more mature techniques. Our framework suggests a range of possible algorithms lying between tree-based search and local search.

Advance reservation of Grid resources can play a key role in enabling Grid middleware to deliver on-demand resource provision with significantly improved Quality-of-Service (QoS). However, in the Grid, advance reservation has been largely ignored due to the dynamic Grid behavior, underutilization concerns, multi-constrained applications, and lack of support for agreement enforcement. These issues force the Grid middleware to make resource allocations at runtime with reduced QoS. To remedy these, we introduce a new, 3-layered negotiation protocol for advance reservation of the Grid resources. We model resource allocation as an on-line strip packing problem and introduce a new mechanism that optimizes resource utilization and QoS constraints while generating the contention-free solutions. The mechanism supports open reservations to deal with the dynamic Grid and provides a practical solution for agreement enforcement. We have implemented a prototype and performed experiments to demonstrate the effectiveness of our approach.

The ability to reduce either the number of variables or clauses in instances of the Satisfiability problem (SAT) impacts the expected computational effort of solving a given instance. This ability can actually be essential for specific and hard classes of instances. The objective of this paper is to propose new simpli cation techniques for Conjunctive Normal Form (CNF) formulas. Experimental results, obtained on representative problem instances, indicate that large simplifications can be observed.