The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Note: Computational complexity of some restricted instances of 3-SAT
Discrete Applied Mathematics
Popular Matchings with Variable Job Capacities
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Popular matchings with variable item copies
Theoretical Computer Science
| Hi-index | 0.05 |
The one-in-three SAT problem is known to be NP-complete even in the absence of negated variables [T.J. Schaefer, The complexity of satisfiability problems, in: Proceedings of the 10th Annual ACM Symposium on Theory of Computing, ACM, New York, 1978, pp. 216-226], a variant known as positive (or monotone) one-in-three SAT. In this note, we use clausal graphs to investigate a further restriction: k-bounded positive one-in-three SAT (kBP one-in-three SAT), in which each variable occurs in no more than k clauses. We show that for k=2, k BP one-in-three SAT is in the polynomial complexity class P, while for all k2, it is NP-complete, providing another way of exploring the boundary between classes P and NP.