Introduction to Circuit Complexity
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This advanced textbook presents a broad and up-to-date view of the computational complexity theory of Boolean circuits. It combines the algorithmic and the computability-based approach, and includes extensive discussion of the literature to facilitate further study.It begins with efficient Boolean circuits for problems with high practical relevance, e.g., arithmetic operations, sorting, and transitive closure, then compares the computational model of Boolean circuits with other models such as Turing machines and parallel machines. Examination of the complexity of specific problems leads to the definition of complexity classes. The theory of circuit complexity classes is then thoroughly developed, including the theory of lower bounds and advanced topics such as connections to algebraic structures and to finite model theory.
Introduction11Complexity Measures and Reductions52Relations to Other Computation Models353Lower Bounds794The NC Hierarchy1075Arithmetic Circuits1736Polynomial Time and Beyond215AppMathematical Preliminaries233Bibliography241List of Figures255Author Index257Subject Index261
