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arXiv · 1511.07813

2-Xor revisited: satisfiability and probabilities of functions

Élie de Panafieu·Danièle Gardy·Bernhard Gittenberger·Markus Kuba
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Abstract

The problem 2-Xor-Sat asks for the probability that a random expression, built as a conjunction of clauses $x \oplus y$, 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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Élie de Panafieu, Danièle Gardy, Bernhard Gittenberger, Markus Kuba. 2015-11-24. 2-Xor revisited: satisfiability and probabilities of functions. https://arxiv.org/abs/1511.07813

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