## Computational complexityThis text offers a comprehensive and accessible treatment of the theory of algorithms and complexity - the elegant body of concepts and methods developed by computer scientists over the past 30 years for studying the performance and limitations of computer algorithms. Among topics covered are: reductions and NP-completeness, cryptography and protocols, randomized algorithms, and approximability of optimization problems, circuit complexity, the "structural" aspects of the P=NP question, parallel computation, the polynomial hierarchy, and many others. Several sophisticated and recent results are presented in a rather simple way, while many more are developed in the form of extensive notes, problems, and hints. The book is surprisingly self-contained, in that it develops all necessary mathematical prerequisites from such diverse fields as computability, logic, number theory, combinatorics and probability. |

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User Review - DJ - Goodreadsrecommended by Scott Aaronson as a conceptual intro to complexity Read full review

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User Review - dead letter office - Goodreadsi'm not aware of too many choices for introductory graduate complexity theory. this one is not great, but it'll work. Read full review

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3SAT accepting Alice axiom binary bits Boolean circuit Boolean expression Boolean functions bound Chapter clauses complete problems complexity classes Computer Science configuration conjunctive normal form coNP Consider construction Corollary corresponding cursor cycle decides define definition deterministic directed graph edges encoding example exponential false Figure finite first-order first-order logic gadget gates given graph G halts HAMILTON PATH IEEE Symp INDEPENDENT SET induction input instance integers L-reduction language Lemma length literals logarithmic space logic matching matrix MAX FLOW MAX-CUT MAXSNP modulo nodes nondeterministic Turing machine normal form Notice number theory optimization problems optimum oracle machine output parallel polynomial hierarchy prime Proc processors proof of Theorem Proposition prove PSPACE PSPACE-complete quantifiers random randomized algorithm REACHABILITY recall recursively enumerable reduction result satisfying truth assignment second-order logic Section sequence Show simulated solved steps string subset Suppose symbol true variables