Probabilities of 2-Xor Functions

Abstract. 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