Conclusions and Open Problems

Abstract

The proof of each one of these results requires new tools and ideas, most notably in discrete Fourier analysis. We believe that the development of these new tools is a key contribution of the research presented herein, and hope that they will be useful in subsequent research to make progress on outstanding challenges in TCS. We conclude this thesis with several open problems. Problem 1 Prove that there exists c > 1 , such that for every ε > 0, GapUG[c, ε] is NP-hard on 2 instances with alphabet size q(ε) ∈ N.