Theory of Computational ComplexityA complete treatment of fundamentals and recent advances in complexity theory Complexity theory studies the inherent difficulties of solving algorithmic problems by digital computers. This comprehensive work discusses the major topics in complexity theory, including fundamental topics as well as recent breakthroughs not previously available in book form. Theory of Computational Complexity offers a thorough presentation of the fundamentals of complexity theory, including NP-completeness theory, the polynomial-time hierarchy, relativization, and the application to cryptography. It also examines the theory of nonuniform computational complexity, including the computational models of decision trees and Boolean circuits, and the notion of polynomial-time isomorphism. The theory of probabilistic complexity, which studies complexity issues related to randomized computation as well as interactive proof systems and probabilistically checkable proofs, is also covered. Extraordinary in both its breadth and depth, this volume: * Provides complete proofs of recent breakthroughs in complexity theory * Presents results in well-defined form with complete proofs and numerous exercises * Includes scores of graphs and figures to clarify difficult material An invaluable resource for researchers as well as an important guide for graduate and advanced undergraduate students, Theory of Computational Complexity is destined to become the standard reference in the field. |
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accepts addition algorithm answer approximation Arthur assignment assume Boolean function bounded called circuit claim clauses complexity complexity classes computation condition configuration consider constant construct contains decision define Definition denote determine deterministic easy edges elements encoding equal error exactly Example Exercise exists Figure find first formula function f gate given graph graph G halts hence hierarchy holds implies input instance integer label least Lemma length machine Merlin monotone moves node Note notion NP-complete observe oracle output path polynomial polynomial-time prime probabilistic probability problem Prove query random bits reducibility rejects relation requirement respectively satisfies satisfying simulation space stage step string Suppose symbol tape Theorem theory tree true Turing variables verifier vertex vertices write