Recognition of q-Horn formulae in linear time
Discrete Applied Mathematics
A perspective on certain polynomial-time solvable classes of satisfiability
Discrete Applied Mathematics
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Solving satisfiability in less than 2n steps
Discrete Applied Mathematics
Parameterized Complexity
A CNF class generalizing exact linear formulas
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
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We study the first level of a conjunctive normal form (CNF) formula hierarchy with respect to the propositional satisfiability problem (SAT). This hierarchy is defined over a base formula that we call a hypercube (formula). Such a hypercube simply consists of all 2n possible n-clauses over a given set of n Boolean variables. The first level of the hierarchy are 1-hyperjoins, meaning that arbitrary hypercubes are joined together via taking from each arbitrary many clauses for joining, i.e., set-union, such that each chosen clause occurs in at most one new clause of the 1-hyperjoin. We prove that arbitrary 1-hyperjoins can efficiently be recognized and solved w.r.t. SAT. To that end we introduce a simple closure concept on the set of the propositional variables of a formula.