## 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, October 09, 2014, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Jan Hazla

## Parallel Repetition from Fortification

I will present a paper by Dana Moshkovitz "Parallel Repetition from Fortification" (FOCS 2014).

The PCP theorem states that there exists some $\epsilon > 0$ such that it is NP-hard to distinguish between two-prover projection games with value $1$ and with value $1-\epsilon$. It can be strengthened to the following: for _every_ $\epsilon > 0$ it is NP-hard to distinguish between games with value $1$ and with value $\epsilon$.

The usual proof of the strong PCP theorem is via the parallel repetition theorem: for every game $G$ with value strictly less than $1$, there exists some $c < 1$ such that the value of the $k$-wise parallel repetition $G^k$ is at most $c^k$. However, despite substantial efforts all known proofs of the parallel repetition theorem are rather involved.

The paper shows a simpler way of proving the strong PCP theorem: given a projection game $G$, we first transform it to a "fortified" game $G'$ with the same value and then prove (easier) parallel repetition theorem for fortified games.

Previous talks by year:   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