## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

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

Duration: 30 minutes

Location: CAB G51

Speaker: Nemanja Skoric

## Hard problems imply efficient derandomization

"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 2c n can not be approximated by a circuit of size 2d n, BPP = P.

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