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

Date and Time: Tuesday, October 29, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Felix Weissenberger

Two-Prover Games for Parallel Repetition

In a two-prover game, a verifier chooses questions (x,y) according to a publicly known distribution. He sends x to Alice and y to Bob. They answer with a(x) and b(y). The game is won if a publicly known predicate V(x,y,a(x),b(y)) is satisfied. The value of the game is the winning probability if Alice and Bob play optimally. In the parallel repetition of a two-prover game, independent copies of the game are played in parallel, and it is won if and only if all copies are won.

Two-prover games and their parallel repetition are motivated by the error reduction of two prover one round proof systems, which are related to the PCP Theorem and inapproximability.

The best parallel repetition theorem states that for a game with value 1- ε, for ε > 0, and answer alphabet size 2^s, the value of its k-fold parallel repetition is at most e^{-f(ε,s) · k}, with f(ε,s)∈ Ω (ε³/s). Moreover, there are two independent examples of games which show that f(ε,s) ∈ O(ε²) and f(ε,s) ∈ O(log(s)/s).

We present a parallel repetition theorem for cycle games where f(ε,s) is independent of s. In cycle games the questions are drawn from the uniform distribution and the question graph is a cycle.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login