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A threshold for unsatisfiability

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

Abstract

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].

Keywords

Random Graph Common Edge Propositional Formula Main Path Simple Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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