The SDP Value for Random Two-Eigenvalue CSPs

Sidhanth Mohanty, Ryan O'Donnell, Pedro Paredes, Markus Bläser, Christophe Paul
2020 Symposium on Theoretical Aspects of Computer Science  
We precisely determine the SDP value (equivalently, quantum value) of large random instances of certain kinds of constraint satisfaction problems, "two-eigenvalue 2CSPs". We show this SDP value coincides with the spectral relaxation value, possibly indicating a computational threshold. Our analysis extends the previously resolved cases of random regular 2XOR and NAE-3SAT, and includes new cases such as random Sort₄ (equivalently, CHSH) and Forrelation CSPs. Our techniques include new
more » ... ions of the nonbacktracking operator, the Ihara-Bass Formula, and the Friedman/Bordenave proof of Alon's Conjecture.
doi:10.4230/lipics.stacs.2020.50 dblp:conf/stacs/MohantyO020 fatcat:ay2heso6hbcm3nyl6tdr2cdqo4