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A Continuous-Discontinuous Second-Order Transition in the Satisfiability of Random Horn-SAT Formulas

  • Cristopher Moore
  • Gabriel Istrate
  • Demetrios Demopoulos
  • Moshe Y. Vardi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3624)

Abstract

We compute the probability of satisfiability of a class of random Horn-SAT formulae, motivated by a connection with the nonemptiness problem of finite tree automata. In particular, when the maximum clause length is three, this model displays a curve in its parameter space along which the probability of satisfiability is discontinuous, ending in a second-order phase transition where it becomes continuous. This is the first case in which a phase transition of this type has been rigorously established for a random constraint satisfaction problem.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Cristopher Moore
    • 1
  • Gabriel Istrate
    • 2
  • Demetrios Demopoulos
    • 3
  • Moshe Y. Vardi
    • 4
  1. 1.Department of Computer ScienceUniversity of New MexicoAlbuquerqueUSA
  2. 2.CCS-5, Los Alamos National LaboratoryLos AlamosUSA
  3. 3.Archimedean AcademyMiamiUSA
  4. 4.Department of Computer ScienceRice UniversityHoustonUSA

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