1-In-3 Vs. Not-All-Equal: Dichotomy of a Broken Promise

The 1-in-3 and Not-All-Equal satisfiability problems for Boolean CNF formulasare 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, weinvestigate this constraint satisfaction problem in a regime where the promiseis weakened from either side by a rainbow-free structure, and establish acomplexity dichotomy for the resulting class of computational problems.