Titlebook: Randomness and Completeness in Computational Complexity; Dieter Melkebeek Book 2000 Springer-Verlag Berlin Heidelberg 2000 Algorithms.Comp

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2. Preliminaries,Computational complexity delineates which problems computers can realistically solve. After describing the notion of a computational problem and giving some important examples, we will formalize the various computer models we will consider. We will introduce relevant resources for each of them and d

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3. Derandomizing Arthur-Merlin Games,ool is relativization: We will show that known hardness versus randomness trade-offs relativize. As a corollary, we obtain that graph nonisomorphism has subexponential size proofs unless the polynomial-time hierarchy collapses. Applications of the same technique to various randomized processes other

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4. Sparseness of Complete Languages,with low density. Our main result establishes the logical completeness of this approach for separating polynomial time from logarithmic space using reductions with a bounded number of queries. Similar techniques apply to various other complexity classes, in the deterministic as well as in the random

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8. The Frequency of Autoreducible Languages,nded measure, as well as within the context of betting games, a notion which we will develop here and which provides an alternate to resourcebounded measure. Several approaches for separating BPP from EXP will come up. problem