Introduction to Mathematics of Satisfiability (Chapman & Hall/CRC Studies in Informatics Series) 1st Edition by Victor W. Marek (PDF)

Description

Although this area has a history of over 80 years, it was not until the creation of efficient SAT solvers in the mid-1990s that it became practically important, finding applications in electronic design automation, hardware and software verification, combinatorial optimization, and more. Exploring the theoretical and practical aspects of satisfiability, Introduction to Mathematics of Satisfiability focuses on the satisfiability of theories consisting of propositional logic formulas. It describes how SAT solvers and techniques are applied to problems in mathematics and computer science as well as important applications in computer engineering.The book first deals with logic fundamentals, including the syntax of propositional logic, complete sets of functors, normal forms, the Craig lemma, and compactness. It then examines clauses, their proof theory and semantics, and basic complexity issues of propositional logic. The final chapters on knowledge representation cover finite runs of Turing machines and encodings into SAT. One of the pioneers of answer set programming, the author shows how constraint satisfaction systems can be worked out by satisfiability solvers and how answer set programming can be used for knowledge representation.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Boolean satisfiability (SAT) is a one of the most important problems in the field of computer science. It is at the heart of a great deal of the theory and practice of much the field. Victor Marek’s experience with the subject comes from being a first-rate researcher and a great teacher of the subject. This book is best suited for teachers, researchers, students, or practitioners of computer science. As such, I use some technical terminology from the field without defining it.There are many poorly written books about computer science, and many books concerning the mathematical fundamentals of the field are written (seemingly) assuming that the reader is a mathematician. This book is written assuming that you know nothing about the field of Boolean satisfiability, however it covers all of the most important topics related to the SAT problem.The first few chapters serve as a survey of all theoretical knowledge, terms, and notation that you will need starting with some of the very basics such as sets, lattices, and permutations. If you have a decent theoretical knowledge you can probably skip some or all of the introductory material and understand the book without issue. I do like that this material is included, however, because it makes the book very self contained.The remaining chapters in the book cover all of the most important preliminaries of logic, representations, algorithms for solving SAT, complexities of the problem, easy subsets of SAT, and constraint satisfaction. This book is easy to read for non mathematicians assuming a solid (at least undergraduate) level of knowledge of computer science preliminaries, discrete math, and theory of computation. Upper-level undergraduates and anyone with at least a bachelors degree in CS should have no problems getting through the material.This book should be on the shelf of every CS professor, particularly those who study or teach logic, CS theory, programming languages or declarative programming, or artificial intelligence. A firm understanding of Boolean satisfiability will give you important insights into the theory of computation, practical and theoretical applications of logic, and declarative programming techniques including the use of SAT solvers and declarative languages such as Prolog.Disclaimer: I do know the author, and studied at the university where he works. I sought this book out before knowing that he had written it. I discovered it in our university library while doing research, and I decided to review it because it is a very high quality reference book. I am writing this review entirely out of my own accord, and I did my bet to remain objective about the content. I was not asked by anyone to write this review. I was not compensated in any way for this review.

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