Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

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

Mittagsseminar Talk Information

Date and Time: Thursday, October 09, 2014, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

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.

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