On the complexity of the approximate hypergraph homomorphism problem

Lorenzo Ciardo, Marcin Kozik, Andrei A. Krokhin, Tamio-Vesa Nakajima, Stanislav Zivný

Abstract: The 1-in-3 and Not-All-Equal satisfiability problems for Boolean CNF formulas are two well-known NP-hard problems. In contrast, the promise 1-in-3 vs. Not-All-Equal problem can be solved in polynomial time. In the present work, we investigate this constraint satisfaction problem in a regime where the promise is weakened from either side by a rainbow-free structure, and establish a complexity dichotomy for the resulting class of computational problems.