Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, November 14, 2013, 12:15 pm

**Duration**: 30 minutes

**Location**: CAB G51

**Speaker**: Nemanja Skoric

"Can randomness help computation?" and "Do natural hard problems exist?" are some of the most important questions in theoretical computer science. It turns out there is a surprising connection between these two.

It is reasonable to think that simulating a probabilistic algorithm with a deterministic one, requires significant loss in efficiency. However, there is evidence that this is not true. Under widely believed assumptions, BPP = P, where BPP is the class of problems computable by randomized polynomial algorithms, with an error probability of at most 1/3. Following a series of papers by Blum. Micali, Yao, Nisan, Wigderson, Impagliazzo et al. it was shown in '97 that if there is a problem computable in deterministic time 2 ^{c n}, for some constant c, which can not be computed by a circuit of size 2 ^{d n}, for some constant d, then BPP = P.

In this talk, we will present a high-level picture of the work by Nisan and Wigderson '94, which shows a weaker statement than the one above. Namely, under the assumption that a problem computable in time 2^{c n} can not be *approximated* by a circuit of size 2^{d n}, BPP = P.

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