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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.

Computer science --- Algebra, Boolean. --- Computational complexity. --- Electronic digital computers --- Logic, Symbolic and mathematical. --- Circuits --- Design. --- Computers. --- Algorithms. --- Mathematical logic. --- Computer mathematics. --- Electronics. --- Microelectronics. --- Theory of Computation. --- Computation by Abstract Devices. --- Algorithm Analysis and Problem Complexity. --- Mathematical Logic and Formal Languages. --- Computational Mathematics and Numerical Analysis. --- Electronics and Microelectronics, Instrumentation. --- Microminiature electronic equipment --- Microminiaturization (Electronics) --- Electronics --- Microtechnology --- Semiconductors --- Miniature electronic equipment --- Electrical engineering --- Physical sciences --- Computer mathematics --- Electronic data processing --- Mathematics --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Algorism --- Algebra --- Arithmetic --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Foundations --- Automatic digital computers --- Computers, Electronic digital --- Digital computers, Electronic --- Computers --- Hybrid computers --- Sequential machine theory