Lower bounds for random 3-SAT via differential equations

  • Achlioptas D
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Abstract

It is widely believed that the probability of satisfiability for random k-SAT formulae exhibits a sharp threshold as a function of their clauses-to-variables ratio. For the most studied case, k=3, there have been a number of results during the last decade providing upper and lower bounds for the threshold's potential location. All lower bounds in this vein have been algorithmic, i.e., in each case a particular algorithm was shown to satisfy random instances of 3-SAT with probability 1-o(1) if the clauses-to-variables ratio is below a certain value. We show how differential equations can serve as a generic tool for analyzing such algorithms by rederiving most of the known lower bounds for random 3-SAT in a simple, uniform manner. © Elsevier Science B.V. All rights reserved.

Author-supplied keywords

  • Algorithms
  • Differential equations
  • Random 3-sat

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Authors

  • Dimitris Achlioptas

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