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We study the asymptotic relation between the probability and the complexity of Boolean functions in the implicational fragment which are generated by large random Boolean expressions involving variables and implication, as the number of variables tends to infinity. In contrast to models studied in the literature so far, we consider two expressions to be… (More)

We define a probability distribution over the set of Boolean functions of k variables induced by the tree representation of Boolean expressions. The law we are interested in is inspired by the growth model of Binary Search Trees: we call it the growing trees law. We study it over different logical systems and compare the results we obtain to already known… (More)

This article is motivated by the following satisfiability question: pick uniformly at random an $$\mathsf {and/or}$$ and / or Boolean expression of length n, built on a set of $$k_n$$ k n Boolean variables. What is the probability that this expression is satisfiable? asymptotically when n tends to infinity? The model of random Boolean expressions developed… (More)

Since the 1990s, the probability distribution on Boolean functions, induced by some random formulas built upon the connectives And and Or, has been intensively studied. These formulas rely on plane binary trees. We extend all the results, in particular the relation between the probability and the complexity of a function, to more general formula structures:… (More)

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