One more occurrence of variables makes satisfiability jump from trivial to NP-complete
SIAM Journal on Computing
A short proof of Fisher's inequality
Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
New algorithms for exact satisfiability
Theoretical Computer Science
On Some SAT-Variants over Linear Formulas
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Linear CNF formulas and satisfiability
Discrete Applied Mathematics
Approximation algorithms and hardness results for the clique packing problem
Discrete Applied Mathematics
Algorithms for variable-weighted 2-SAT and dual problems
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
XSAT and NAE-SAT of linear CNF classes
Discrete Applied Mathematics
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We investigate the computational complexity of the exact satisfiability problem (XSAT) restricted to certain subclasses of linear CNF formulas. These classes are defined through restricting the number of occurrences of variables and are therefore interesting because the complexity status does not follow from Schaefer’s theorem [14,7]. Specifically we prove that XSAT remains NP-complete for linear formulas which are monotone and all variables occur exactly l times. We also present some complexity results for exact linear formulas left open in [9]. Concretely, we show that XSAT for this class is NP-complete, in contrast to SAT or NAE-SAT. This can also be established when clauses have length at least k, for fixed integer k≥3. However, the XSAT-complexity for exact linear formulas with clause length exactly k remains open, but we provide its polynomial-time behaviour at least for every positive integer k≤6.