December 14, 2016

2-Xor Revisited: Satisfiability and Probabilities of Functions

  • De Panafieu E.
  • Gardy D.
  • Gittenberger B.
  • Kuba M.

The problem 2-Xor-Sat asks for the probability that a random expression, built as a conjunction of clauses , is satisfiable. We revisit this classical problem by giving an alternative, explicit expression of this probability. We then consider a refinement of it, namely the probability that a random expression computes a specific Boolean function. The answers to both problems involve a description of 2-Xor expressions as multigraphs and use classical methods of analytic combinatorics by expressing probabilities through coefficients of generating functions.

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