Write a "random" boolean expression, built from a conjunction of Xor
clauses on
a finite number $n$ of boolean variables: what is the probability that such an
expression, chosen randomly, is satisfiable? i.e., that it (does not) computes
the constant function False?
Our approach to this classical problem is, starting from a uniform probability
distribution on these boolean expressions, to define and compute
asymptotically
the probability distribution induced on the set of all boolean functions.
Writing down a system of equations on the generating functions
associated to the
boolean functions, we use the structure of the dependencies between boolean
functions to analyze this system and gain information on the structure of its
set of singularities, thus opening the way to asymptotic analysis of the
probabilities.

Work in common with Bernhard Gittenberger and Markus Kuba.