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Random Horn formulas and propagation connectivity for directed hypergraphs

Abstract : 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).
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Robert H. Sloan, Despina Stasi, György Turán. Random Horn formulas and propagation connectivity for directed hypergraphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2012, Vol. 14 no. 2 (2), pp.29--35. ⟨hal-00990587⟩

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