Before revision:  Our positive results show wider applicability of bias-based algorithms used previously by Guruswami-Velingker-Velusamy APPROX'17 , Chou-Golovnev-Velusamy FOCS'20 by giving a systematic way to explore biases. Our negative results combine the Fourier analytic methods of Kapralov-Khanna-Sudan SODA'15 , which we extend to a wider class of CSPs, with a rich collection of reductions among communication complexity problems that lie at the heart of the negative results .
After revision:  Our positive results show wider applicability of bias-based algorithms used previously by Guruswami-Velingker-Velusamy APPROX'17 , Chou-Golovnev-Velusamy FOCS'20  Kapralov-Khanna-Sudan SODA'15 , which we extend to a wider class of CSPs, with a rich collection of reductions among communication complexity problems that lie at the heart of the negative results .