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Typical case complexity of satisfiability algorithms and the threshold phenomenon
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Domain permutation reduction for constraint satisfaction problems
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Known and new classes of generalized Horn formulae with polynomial recognition and SAT testing
Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
A sharp threshold for the renameable-Horn and the q-Horn properties
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Typical case complexity of Satisfiability Algorithms and the threshold phenomenon
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On the boolean connectivity problem for horn relations
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The class of Horn clause sets in propositional logic is extended to a larger class for which the satisfiability problem can still be solved by unit resolution in linear time. It is shown that to every arborescence there corresponds a family of extended Horn sets, where ordinary Horn sets correspond to stars with a root at the center. These results derive from a theorem of Chandresekaran that characterizes when an integer solution of a system of inequalities can be found by rounding a real solution in a certain way. A linear-time procedure is provided for identifying “hidden” extended Horn sets (extended Horn but for complementation of variables) that correspond to a specified arborescence. Finally, a way to interpret extended Horn sets in applications is suggested.