Random 2-SAT and unsatisfiability. (English) Zbl 0999.68086
Summary: It is known that almost all 2-CNF formulas with \(n(1+\varepsilon)\) clauses are not satisfiable, \(\varepsilon>0\) a constant and \(n\) the number of variables. We strengthen this result, showing that it still holds with \(\varepsilon=\varepsilon(n)\geq w(n)n^{-1/4}\), where \(w(n)\) is any function that tends to infinity as \(n\) tends to infinity.
MSC:
| 68Q25 | Analysis of algorithms and problem complexity |
| 68R05 | Combinatorics in computer science |
| 03B05 | Classical propositional logic |
Keywords:
2-CNF formulasReferences:
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