A threshold for unsatisfiability
We show the following threshold property of satisfiability of propositional formulas in 2-CNF: If C = 1+ε where ε > 0 is fixed, then almost all formulas in 2-CNF with C · n different clauses over n variables are unsatisfiable. If C = 1 - ε, then almost all such formulas are satisfiable. (”Almost all” simply means that the probability w.r.t. the uniform distribution considered here tends to 1 as n → ∞.) Due to the close relationship between satisfiability of formulas in 2-CNF and graph theoretic properties it is not surprising that our proof uses techniques from the theory of random graphs, in particular .
KeywordsRandom Graph Common Edge Propositional Formula Main Path Simple Cycle
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