Theory of Computing
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Title     : Towards a Proof of the $2$-to-$1$ Games Conjecture
Authors   : Irit Dinur, Subhash Khot, Guy Kindler, Dor Minzer, and Muli Safra
Volume    : 21
Number    : 11
Pages     : 1-50
URL       : https://theoryofcomputing.org/articles/v021a011

Abstract
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We propose a combinatorial hypothesis regarding a subspace vs.
subspace agreement test, and prove that if correct it leads to a proof
of the $2$-to-$1$ Games Conjecture, albeit with imperfect completeness.
This paper presents the second installment in a line of work by various
subsets of the authors (with additional contributions by Barak, Kothari,
and Steurer (ITCS'19)), which led to a proof of the
$2$-to-$2$ Games Conjecture.


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A preliminary version of this paper appeared in the Proceedings
of the 50th ACM Symposium on Theory of Computing (STOC'18).