Editing Boolean satisfiability problem (section)

===Not-all-equal 3-satisfiability===
{{main|Not-all-equal 3-satisfiability}}
Another variant is the '''not-all-equal 3-satisfiability''' problem (also called '''NAE3SAT'''). Given a conjunctive normal form with three literals per clause, the problem is to determine if an assignment to the variables exists such that in no clause all three literals have the same truth value. This problem is NP-complete, too, even if no negation symbols are admitted, by Schaefer's dichotomy theorem.<ref name="schaefer">{{Cite conference | last1 = Schaefer | first1 = Thomas J. | year = 1978 | title = The complexity of satisfiability problems | book-title = Proceedings of the 10th Annual ACM Symposium on Theory of Computing | place = San Diego, California | pages = 216–226 | url = http://www.ccs.neu.edu/home/lieber/courses/csg260/f06/materials/papers/max-sat/p216-schaefer.pdf |doi=10.1145/800133.804350 |citeseerx=10.1.1.393.8951 }}</ref>