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This textbook presents a survey of research on boolean functions, circuits, parallel computation models, function algebras, and proof systems. Its main aim is to elucidate the structure of “fast” parallel computation. The complexity of parallel computation is emphasized through a variety of techniques ranging from finite combinatorics, probability theory and finite group theory to finite model theory and proof theory. Nonuniform computation models are studied in the form of boolean circuits; uniform ones in a variety of forms. Steps in the investigation of non-deterministic polynomial time are surveyed as is the complexity of various proof systems. The book will benefit advanced undergraduates and graduate students as well as researchers in the field of complexity theory.
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