eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2015-08-13
497
511
10.4230/LIPIcs.APPROX-RANDOM.2015.497
article
On Fortification of Projection Games
Bhangale, Amey
Saptharishi, Ramprasad
Varma, Girish
Venkat, Rakesh
A recent result of Moshkovitz [Moshkovitz14] presented an ingenious method to provide a completely elementary proof of the Parallel Repetition Theorem for certain projection games via a construction called fortification. However, the construction used in [Moshkovitz14] to fortify arbitrary label cover instances using an arbitrary extractor is insufficient to prove parallel repetition. In this paper, we provide a fix by using a stronger graph that we call fortifiers. Fortifiers are graphs that have both l_1 and l_2 guarantees on induced distributions from large subsets.
We then show that an expander with sufficient spectral gap, or a bi-regular extractor with stronger parameters (the latter is also the construction used in an independent update [Moshkovitz15] of [Moshkovitz14] with an alternate argument), is a good fortifier. We also show that using a fortifier (in particular l_2 guarantees) is necessary for obtaining the robustness required for fortification.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol040-approx-random2015/LIPIcs.APPROX-RANDOM.2015.497/LIPIcs.APPROX-RANDOM.2015.497.pdf
Parallel Repetition
Fortification