A threshold for unsatisfiability

  • Andreas Goerdt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 629)


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 [12].


Random Graph Common Edge Propositional Formula Main Path Simple Cycle 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Andreas Goerdt
    • 1
  1. 1.FB 17/Mathematik-InformatikUniversität -GH- PaderbornPaderborn

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