The satisfiability problem of propositional logic, SAT for short, is the first algorithmic problem that was shown to be NP-complete, and is the cornerstone of virtually all NP-completeness proofs. The SAT problem consists of deciding whether a given Boolean formula has a “solution”, in the sense of an assignment to the variables making the entire formula to evaluate to true. Over the last few years very powerful algorithms have been devised being able to solve SAT problems with hundreds of thousands of variables. For difficult (or randomly generated) formulas these algorithms can be compared to the proverbial search for the needle in a haystack. This book explains how such algorithms work, for example, by exploiting the structure of the SAT problem with an appropriate logical calculus, like resolution. But also algorithms based on “physical” principles are considered. I was delighted to see how nicely the authors were able to cover such a variety of topics with elegance. I cannot resist saying that the introduction to SAT on page 9 is absolutely the best I ever expect to see in any book! Donald E. Knuth, Stanford University This book gives lucid descriptions of algorithms for SAT that are better than you would think! A must-read for anyone in theory. William Gasarch, University of Maryland It was a wonderful surprise to see a deep mathematical analysis of important algorithms for SAT presented so clearly and concisely. This is an excellent introductory book for studying the foundations of constraint satisfaction. Osamu Watanabe, Tokyo Institute of Technology

Propositional logic has been recognized throughout the centuries as one of the cornerstones of reasoning in philosophy and mathematics. Over time, its formalization into Boolean algebra was accompanied by the recognition that a wide range of combinatorial problems can be expressed as propositional satisfiability (SAT) problems. Because of this dual role, SAT developed into a mature, multi-faceted scientific discipline, and from the earliest days of computing a search was underway to discover how to solve SAT problems in an automated fashion. This book, the Handbook of Satisfiability, is the second, updated and revised edition of the book first published in 2009 under the same name. The handbook aims to capture the full breadth and depth of SAT and to bring together significant progress and advances in automated solving. Topics covered span practical and theoretical research on SAT and its applications and include search algorithms, heuristics, analysis of algorithms, hard instances, randomized formulae, problem encodings, industrial applications, solvers, simplifiers, tools, case studies and empirical results. SAT is interpreted in a broad sense, so as well as propositional satisfiability, there are chapters covering the domain of quantified Boolean formulae (QBF), constraints programming techniques (CSP) for word-level problems and their propositional encoding, and satisfiability modulo theories (SMT). An extensive bibliography completes each chapter. This second edition of the handbook will be of interest to researchers, graduate students, final-year undergraduates, and practitioners using or contributing to SAT, and will provide both an inspiration and a rich resource for their work. Edmund Clarke, 2007 ACM Turing Award Recipient: "SAT solving is a key technology for 21st century computer science." Donald Knuth, 1974 ACM Turing Award Recipient: "SAT is evidently a killer app, because it is key to the solution of so many other problems." Stephen Cook, 1982 ACM Turing Award Recipient: "The SAT problem is at the core of arguably the most fundamental question in computer science: What makes a problem hard?"

The satisfiability (SAT) problem is central in mathematical logic and computing theory, representing a core of computationally intractable NP-complete problems. It is a fundamental hurdle in solving many problems in automated reasoning, computer-aided design, computer-aided manufacturing, machine vision, database construction and maintenance, robotics, scheduling, integrated circuit design, computer architecture design, and computer networking. Efficient methods for solving the SAT problem play an important role in the development of practical computing systems. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and other practical new techniques have been developed for solving the SAT problem. This book describes these state-of-the-art methods, both sequential and parallel, and discusses tradeoffs and limitations in the rapidly growing field of satisfiability testing. It will be useful for computer theorists, algorithmists, and practitioners working in all areas in computer science, computer engineering, operations research, and applied logic.

Surveys the recently discovered lower bounds for the time and space complexity of satisfiability and closely related problems. It overviews the state-of-the-art results on general deterministic, randomized, and quantum models of computation, and presents the underlying arguments in a unified framework.

The satisfiability (SAT) problem is central in mathematical logic, computing theory, and many industrial applications. There has been a strong relationship between the theory, the algorithms, and the applications of the SAT problem. This book aims to bring together work by the best theorists, algorithmists, and practitioners working on the sat problem and on industrial applications, as well as to enhance the interaction between the three research groups. The book features the applications of theoretical/algorithmic results to practical problems and presents practical examples for theoretical/algoritmic study. Major topics covered in the book include practical and industial SAT problems and benchmarks, significant case studies and applications of the SAT problem and SAT algorithms, new algorithms and improved techniques for satisfiability testing, specific data structures and implementation details of the SAT algorithms, and the theoretical study of the SAT problem and SAT algorithms.

Stochastic local search (SLS) algorithms are among the most prominent and successful techniques for solving computationally difficult problems. Offering a systematic treatment of SLS algorithms, this book examines the general concepts and specific instances of SLS algorithms and considers their development, analysis and application.

This volume contains the papers presented at the Sixth International Conference on Logic for Programming and Automated Reasoning (LPAR'99), held in Tbilisi, Georgia, September 6-10, 1999, and hosted by the University of Tbilisi. Forty-four papers were submitted to LPAR'99. Each of the submissions was reviewed by three program committee members and an electronic program com mittee meeting was held via the Internet. Twenty-three papers were accepted. We would like to thank the many people who have made LPAR'99 possible. We are grateful to the following groups and individuals: to the program committee and the additional referees for reviewing the papers in a very short time, to the organizing committee, and to the local organizers of the INTAS workshop in Tbilisi in April 1994 (Khimuri Rukhaia, Konstantin Pkhakadze, and Gela Chankvetadze). And last but not least, we would like to thank Konstantin - rovin, who maintained the program committee Web page; Uwe Waldmann, who supplied macros for these proceedings and helped us to install some programs for the electronic management of the program committee work; and Bill McCune, who implemented these programs.

The Best of ICCAD marks the 20th anniversary of the International Conference on Computer Aided Design. This book presents a selection of papers from among the best contributions presented in ICCAD based on their impact on research and applications. The Best of ICCAD contains overview articles solicited from leading EDA researchers that comment on the historical context of the selected papers and outline their impact on follow up work. Nine leading companies including Cadence, Synopsys, Fujitsu, IBM and Magma offer "Industry Viewpoints" outlining the impact of ICCAD on their businesses. The Best of ICCAD provides an insightful reminder on how much progress has been made in EDA in the past twenty years and will be a useful tool for professionals in the field and students in the pursuit to crack the next wave of emerging EDA problems.

For a long time computer scientists have distinguished between fast and slow algo rithms. Fast (or good) algorithms are the algorithms that run in polynomial time, which means that the number of steps required for the algorithm to solve a problem is bounded by some polynomial in the length of the input. All other algorithms are slow (or bad). The running time of slow algorithms is usually exponential. This book is about bad algorithms. There are several reasons why we are interested in exponential time algorithms. Most of us believe that there are many natural problems which cannot be solved by polynomial time algorithms. The most famous and oldest family of hard problems is the family of NP complete problems. Most likely there are no polynomial time al gorithms solving these hard problems and in the worst case scenario the exponential running time is unavoidable. Every combinatorial problem is solvable in ?nite time by enumerating all possi ble solutions, i. e. by brute force search. But is brute force search always unavoid able? De?nitely not. Already in the nineteen sixties and seventies it was known that some NP complete problems can be solved signi?cantly faster than by brute force search. Three classic examples are the following algorithms for the TRAVELLING SALESMAN problem, MAXIMUM INDEPENDENT SET, and COLORING.