Random Horn formulas and propagation connectivity for directed hypergraphs
Authors: Robert H. Sloan 1; Despina Stasi 1; György Turán 1,2,3
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Robert H. Sloan;Despina Stasi;György Turán
1 Departement of Computer Science [UIC]
2 Hungarian Academy of Sciences
3 MTA-SZTE Research Group on Artificial Intelligence
We consider the property that in a random definite Horn formula of size-3 clauses over n variables, where every such clause is included with probability p, there is a pair of variables for which forward chaining produces all other variables. We show that with high probability the property does not hold for p <= 1/(11n ln n), and does hold for p >= (5 1n ln n)/(n ln n).