License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2016.42
URN: urn:nbn:de:0030-drops-66657
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6665/
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Moshkovitz, Dana ; Ramnarayan, Govind ; Yuen, Henry

A No-Go Theorem for Derandomized Parallel Repetition: Beyond Feige-Kilian

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Abstract

In this work we show a barrier towards proving a randomness-efficient parallel repetition, a promising avenue for achieving many tight inapproximability results. Feige and Kilian (STOC'95) proved an impossibility result for randomness-efficient parallel repetition for two prover games with small degree, i.e., when each prover has only few possibilities for the question of the other prover. In recent years, there have been indications that randomness-efficient parallel repetition (also called derandomized parallel repetition) might be possible for games with large degree, circumventing the impossibility result of Feige and Kilian. In particular, Dinur and Meir (CCC'11) construct games with large degree whose repetition can be derandomized using a theorem of Impagliazzo, Kabanets and Wigderson (SICOMP'12). However, obtaining derandomized parallel repetition theorems that would yield optimal inapproximability results has remained elusive.

This paper presents an explanation for the current impasse in progress, by proving a limitation on derandomized parallel repetition. We formalize two properties which we call "fortification-friendliness" and "yields robust embeddings". We show that any proof of derandomized parallel repetition achieving almost-linear blow-up cannot both (a) be fortification-friendly and (b) yield robust embeddings. Unlike Feige and Kilian, we do not require the small degree assumption.

Given that virtually all existing proofs of parallel repetition, including the derandomized parallel repetition result of Dinur and Meir, share these two properties, our no-go theorem highlights a major barrier to achieving almost-linear derandomized parallel repetition.

BibTeX - Entry

@InProceedings{moshkovitz_et_al:LIPIcs:2016:6665,
  author =	{Dana Moshkovitz and Govind Ramnarayan and Henry Yuen},
  title =	{{A No-Go Theorem for Derandomized Parallel Repetition: Beyond Feige-Kilian}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)},
  pages =	{42:3--42:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-018-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{60},
  editor =	{Klaus Jansen and Claire Mathieu and Jos{\'e} D. P. Rolim and Chris Umans},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6665},
  URN =		{urn:nbn:de:0030-drops-66657},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2016.42},
  annote =	{Keywords: Derandomization, parallel repetition, Feige-Killian, fortification}
}

Keywords: Derandomization, parallel repetition, Feige-Killian, fortification
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)
Issue Date: 2016
Date of publication: 06.09.2016

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