Information Processing Letters
Acta Informatica
One more occurrence of variables makes satisfiability jump from trivial to NP-complete
SIAM Journal on Computing
Recognition of q-Horn formulae in linear time
Discrete Applied Mathematics
On finding solutions for extended Horn formulas
Information Processing Letters
Renaming a Set of Clauses as a Horn Set
Journal of the ACM (JACM)
Propositional Logic: Deduction and Algorithms
Propositional Logic: Deduction and Algorithms
A perspective on certain polynomial-time solvable classes of satisfiability
Discrete Applied Mathematics
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Satisfiability of mixed Horn formulas
Discrete Applied Mathematics
Solving satisfiability in less than 2n steps
Discrete Applied Mathematics
A CNF formula hierarchy over the hypercube
AI'07 Proceedings of the 20th Australian joint conference on Advances in artificial intelligence
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
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
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The fibre view on clause sets, previously introduced in [12], is used in the present paper to define and investigate subclasses of CNF that appear to be polynomial time solvable w.r.t. SAT. The most interesting of these classes is a generalization of exact linear formulas, namely formulas such that each pair of distinct clauses has all variables in common or exactly one. By definition, in an exact linear formula each pair of distinct clauses has exactly one variable in common. SAT-solving for exact linear formulas was shown to be easy in [14]. Here we provide an algorithm solving the decision and counting variants of SAT for the generalized class in polynomial time. Moreover we study some other structurally defined formula classes on the basis of the fibre view. We show that these classes have the property that their members all are satisfiable or all are unsatisfiable.