For any odd integer q > 1, we improve the lower bound for general q-query locally decodable codes C: {0,1}^n -> {0,1}^m from m = Omega(n/log n)^{(q+1)/(q-1)} to m = Omega(n^{(q+1)/(q-1)})/log n. For example, for q = 3 we improve the previous bound from Omega(n^2/log^2 n) to Omega(n^2/log n). For ... more >>>

We show that for each k > 0, MA/1 (MA with 1 bit of advice) does not have circuits of size n^k. This implies the first superlinear circuit lower bounds for the promise versions of the classes MA, AM and ZPP_{||}^{NP}.

We extend our main result in several ways. For ... more >>>

We survey time hierarchies, with an emphasis on recent attempts to prove hierarchies for semantic classes.

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