1-in-3 vs. Not-All-Equal: Dichotomy of a broken promise
Computational Complexity
2025-05-09 v3 Discrete Mathematics
Data Structures and Algorithms
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.
Keywords
Cite
@article{arxiv.2302.03456,
title = {1-in-3 vs. Not-All-Equal: Dichotomy of a broken promise},
author = {Lorenzo Ciardo and Marcin Kozik and Andrei Krokhin and Tamio-Vesa Nakajima and Stanislav Živný},
journal= {arXiv preprint arXiv:2302.03456},
year = {2025}
}
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Full version of a LICS 2024 paper