eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-12-07
36:1
36:12
10.4230/LIPIcs.ISAAC.2016.36
article
A Gap Trichotomy for Boolean Constraint Problems: Extending Schaefer's Theorem
Ham, Lucy
In this paper, we investigate "gap problems", which are promise problems where YES instances are flexibly satisfiable in a certain sense, and NO instances are not satisfiable at all. These gap problems generalise a family of constraint-related decision problems, including the constraint satisfaction problem itself, the separation problem (can distinct variables be validly assigned distinct values?) and the 2-robust satisfiability problem (does any assignment on two variables extend to a full satisfying assignment?). We establish a Gap Trichotomy Theorem, which on Boolean domains, completely classifies the complexity of the gap problems considered. As a consequence, we obtain several well-known dichotomy results, as well as dichotomies for the separation problem and the 2-robust satisfiability problem: all are either polynomial-time tractable or NP-complete. Schaefer’s original dichotomy is a notable particular case.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol064-isaac2016/LIPIcs.ISAAC.2016.36/LIPIcs.ISAAC.2016.36.pdf
Constraint Satisfaction Problem
Robust satisfiability
Clone theory
Dichotomy
Trichotomy
Boolean