Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, January 29, 2008, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Dominik Scheder

Hardness, Pseudo-Randomness and Derandomization (Part I)

The ultimate goal of derandomisation theory is to obtain general method to derandomize *every* BPP algorithm (i.e., polynomial time randomized algorithm). The core idea is to feed the randomized Turing machine not with perfect random bits, but bits that look random to it, though they are generated by a pseudo-random generator.

A crucial result is that good random generators can be built using certain hard languages, that is, languages that have exponential complexity on Turing machines as well as for Boolean circuits. It is not known whether such languages exist: Note that every language has at most exponential circuit complexity, but may well have super-exponential complexity on Turing machines.

This result is surprising because it connects a positive complexity result, i.e. possibility of derandomizing all BPP algorithms, with a negative complexity result, namely the existence of certain hard languages.

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