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This is a branch that includes: computational complexity theory; complexity classes, NP-completeness and other completeness concepts; oracle analogues of complexity classes; complexity-theoretic computational models; regular languages; context-free languages; Komolgorov Complexity and so on.

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Derandomizing BPP (bounded-error probabilistic polynomial time)

What's the best result about derandomizing BPP which based on some uniform assumptions? For instance, has someone proved that BPP can be simulated in subexp time if EXP $\not =$ BPP?
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