[Colloquium] Re: [Faculty] Theory Seminars at Computer Science

[Alexander Razborov via Colloquium]

Hi Donna,

Does Andrej have a hotel reservation (he said he had not received any
confirmation)?

Thank you,
Sasha

> On Apr 6, 2017, at 8:12 AM, Donna Brooms via Colloquium via faculty <faculty at mailman.cs.uchicago.edu> wrote:
> 
> Combinatorics & Theoretical Seminar
>  
> Tuesday, April 18, 2017
> Ryerson 251 @ 3pm
> 
> Andrej Bogdanov
> Chinese University of Hong Kong
> http://www.cs.washington.edu/homes/jrl/
> 
> Title: “Small bias requires large formulas”
> A small-biased function is a randomized function whose distribution of truth-tables is small-biased. We show that known explicit lower bounds on the size of (1) general Boolean formulas, (2) Boolean formulas of fan-in two, (3) de Morgan formulas, as well as (4) correlation lower bounds against small de Morgan formulas apply to small-biased functions. As a consequence, any strongly explicit small-biased generator is subject to the best known explicit formula lower bounds in all these models.
> 
> On the other hand, we give a construction of a small-biased function that is tight with respect to lower bounds (1) and (2) for the relevant range of parameters. We interpret this construction as a natural-like barrier against substantially stronger lower bounds for general formulas.
> 
> Host:  Prof. Alexander Razborov
> 
> Refreshments will be served before the talk in Ry 255.
> 
>  
> 
>  
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