“Decision Procedures: An Algorithmic Point of View,” by Daniel Kroening and Ofer Strichman, Springer-Verlag, 2008

The topic of this book is decision procedures for first-order theories, a research area now typically referred to as Satisf iability Modulo Theories (SMT).1 The book is important if for no other reason than because it is one of the first to capture the essential concepts of SMT in a book.2 More importantly, most of the content is still relevant to those wishing to understand the area today. The book is structured as follows. After a high-level introductory chapter, and a chapter on propositional logic and Boolean satisfiability (SAT), the bulk of the content (chapters 3 through 8) deals with decision procedures for specific first-order theories: equality with uninterpreted functions (chapters 3 and 4), linear arithmetic (chapter 5), bit vectors (chapter 6), arrays (chapter 7), and pointer logic (chapter 8). Chapter 9 covers quantifiers (the other chapters focus on quantifier-free formulas); chapter 10 covers theory combination; and chapter 11 describes how to integrate Boolean satisfiability with theory reasoning. In addition, each chapter includes a challenging set of problem exercises. And every chapter except for the first and third concludes with a short but informative “Bibliographic Notes” section which gives some historical context and additional reading for the chapter. Finally, there are two appendices: the first is a single page which mentions the SMT-LIB initiative and some other SMT community activities; and the second is a description of a software library (available online) developed for the book. In this review, I will describe each of the chapters briefly and then conclude with some general remarks about the book.