Probabilities of 2-Xor Functions

  • Élie de Panafieu
  • Danièle Gardy
  • Bernhard Gittenberger
  • Markus Kuba
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)


The problem 2-Xor-Sat asks for the probability that a random expression, built as a conjunction of clauses x ⊕ y, is satisfiable. We consider here a refinement of this question, namely the probability that a random expression computes a specific Boolean function. The answer involves a description of 2-Xor expressions as multigraphs, and uses classical methods of analytic combinatorics.


multigraphs probability of Boolean functions 2-Xor expressions 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Élie de Panafieu
    • 1
  • Danièle Gardy
    • 2
  • Bernhard Gittenberger
    • 3
  • Markus Kuba
    • 3
  1. 1.Sorbonne Paris Cité, LIAFA, UMR 7089Univ. Paris DiderotParisFrance
  2. 2.PRISMUniv. of VersaillesFrance
  3. 3.Institute of Discrete Mathematics and GeometryTU WienAustria

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