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2-Xor revisited: satisfiability and probabilities of functions. (English) Zbl 1352.68193
Summary: 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.

68R05 Combinatorics in computer science
06E30 Boolean functions
68Q87 Probability in computer science (algorithm analysis, random structures, phase transitions, etc.)
Full Text: DOI
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