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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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IV.20 Computational Complexity

Oded Goldreich and Avi Wigderson

1 Algorithms and Computation

This article is concerned with what can be computed efficiently, and what cannot. We will introduce several important concepts and research areas, such as formal models of computation, measures of efficiency, the Image versus ImageImage question, NP-completeness, circuit complexity, proof complexity, randomized computation, pseudorandomness, probabilistic proof systems, ...

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