Work

1 -in- 3 vs . N ot -A ll -E qual : Dichotomy of a Broken Promise

Year: 2025

Type: article

Abstract: The 1 -in- 3 and N ot -A ll -E qual satisfiability problems for Boolean CNF formulas are two well-known NP -hard problems. In contrast, the promise 1 -in- 3 vs . N ot -A ll -E qual 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.

Source: ACM Transactions on Computational Logic

DOI: 10.1145/3719007

Authors: Lorenzo Ciardo, Marcin Kozik, Andrei Krokhin, Tamio-Vesa Nakajima, Stanislav Živný

Institutions: University of Oxford, Jagiellonian University, Durham University

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Funders: UK Research and Innovation, Narodowym Centrum Nauki, Engineering and Physical Sciences Research Council, Clarendon Fund

Awards: Promise Constraint Satisfaction Problem: Structure and Complexity, New Approaches to Approximability of Satisfiable Problems, G8702647912