Computational Complexity: A Conceptual Perspective by Oded Goldreich

By Oded Goldreich

This ebook deals a accomplished standpoint to fashionable subject matters in complexity thought, that is a vital box of the theoretical foundations of laptop technology. It addresses the looming query of what could be completed inside of a restricted period of time without or with different constrained average computational assets. can be utilized as an advent for complex undergraduate and graduate scholars as both a textbook or for self-study, or to specialists, because it presents expositions of many of the sub-areas of complexity idea similar to hardness amplification, pseudorandomness and probabilistic evidence structures.

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In an attempt to keep the bibliographic list from becoming longer than an average chapter, we omitted many relevant references. One trick used toward this end is referring to lists of references in other texts, especially when the latter are cited anyhow. Indeed, our choices of references were biased in favor of textbooks and survey articles, because we believe that they provide the best way to further learn about a research direction and/or approach. We tried, however, not to omit references to key papers in an area.

On the topic of expander graphs, the appendix contains a review of the standard definitions and properties as well as a presentation of the Margulis-Gabber-Galil and the Zig-Zag constructions. Appendix F: Some Omitted Proofs. This appendix contains some proofs that are beneficial as alternatives to the original and/or standard presentations. Included are proofs that PH is reducible to #P via randomized Karp-reductions, and that IP( f ) ⊆ AM(O( f )) ⊆ AM( f ). Appendix G: Some Computational Problems.

For a host of cryptographic applications). Chapter 8: Pseudorandom Generators. The pivot of this chapter is the notion of computational indistinguishability and corresponding notions of pseudorandomness. The definition of general-purpose pseudorandom generators (running in polynomial time and withstanding any polynomial-time distinguisher) is presented as a special case of a general paradigm. The chapter also contains a presentation of other instantiations of the latter paradigm, including generators aimed at derandomizing complexity classes such as BPP, generators withstanding space-bounded distinguishers, and some special-purpose generators.

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