Combinatorics: set systems, hypergraphs, families of vectors, and combinatorial probability
Combinatorics: set systems, hypergraphs, families of vectors, and combinatorial probability
A short proof of Fisher's inequality
Discrete Mathematics
Discrete Mathematics
A perspective on certain polynomial-time solvable classes of satisfiability
Discrete Applied Mathematics
An O (N2.5) algorithm for maximum matching in general graphs
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
A CNF class generalizing exact linear formulas
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Parameterized Complexity
On Some SAT-Variants over Linear Formulas
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
On Some Aspects of Mixed Horn Formulas
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Complexity results for linear XSAT-Problems
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
XSAT and NAE-SAT of linear CNF classes
Discrete Applied Mathematics
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In this paper, we study linear CNF formulas generalizing linear hypergraphs under combinatorial and complexity theoretical aspects w.r.t. SAT. We establish NP-completeness of SAT for the unrestricted linear formula class, and we show the equivalence of NP-completeness of restricted uniform linear formula classes w.r.t. SAT and the existence of unsatisfiable uniform linear witness formulas. On that basis we prove NP-completeness of SAT for uniform linear classes in a resolution-based manner by constructing large-sized formulas. Interested in small witness formulas, we exhibit some combinatorial features of linear hypergraphs closely related to latin squares and finite projective planes helping to construct rather dense, and significantly smaller unsatisfiable k-uniform linear formulas, at least for the cases k=3,4.