Boolean models and methods have many applications in mathematics, science, and engineering. This book is a collection of papers on Boolean models and methods. It includes contributions by experts from around the world. Its target audience consists of students, research workers, and engineers. Another book by the same editors [1] covers the basics required for understanding the material in this book.

The book consists of five parts: “Algebraic Structures,” “Logic,” “Learning Theory and Cryptography,” “Graph Representations and Efficient Computation Models,” and “Applications in Engineering.”

Part 1 deals with the composition and decomposition of Boolean functions. It also introduces the concept of clones of Boolean functions.

Part 2 covers topics in logic such as proof theory, probabilistic analysis of satisfiability algorithms, and optimization methods used in logic. This part covers several important proof systems for propositional logic, equational calculus, axiomatic proof systems, sequent calculus, and resolution proofs. It also examines the efficiency of a given algorithm when applied to a random satisfiability instance. In addition, this part of the book examines difficult as well as easy instances. The section on optimization methods in logic concentrates on the application of mathematical programming methods for the solution of Boolean inference and satisfiability problems.

Part 3 covers learning theory and cryptography. The topics addressed in this part include probabilistic learning and Boolean functions, learning Boolean functions with queries, and the use of Boolean functions for error-correcting codes and cryptography.

Graph representations and efficient computation models are discussed in Part 4. Binary decision diagrams--graph representations of functions that have many applications for estimating the algorithmic complexity of problems--are addressed, as are Boolean functions, which have been widely used in circuit complexity. Boolean circuits, useful models for the hardware realization of Boolean functions that play a major role in complexity theory, are also discussed. This part also covers Fourier transforms, which have been found useful for analyzing problems in discrete mathematics. Neural networks and Boolean functions are also addressed in this part.

The fifth and final part of the book focuses on applications of Boolean models and methods in engineering. The chapter on hardware equivalence and property verification investigates the equivalence of any two Boolean circuits. The chapter on the synthesis of multilevel Boolean networks studies techniques to minimize the physical area occupied by Boolean circuits. The last chapter of the book is on Boolean aspects of network reliability, and reviews exact methods for reliability computations.

The book is quite voluminous, and exceeds 750 pages. Specialists in various areas have authored chapters on their respective topics. The book includes adequate references to the literature at the chapter ends. It does not have an index, however, and does not include any exercises for pedagogic purposes. Additionally, the back cover is not readable. On the other hand, the book is well written, and its homogeneous presentation is laudable. The authors have written the chapters so that readers may read them independently of each other, if desired.

On the whole, this is a useful book that will serve as a textbook and reference. It is appropriate for a one- or two-semester course on Boolean models and methods. I strongly recommend it.