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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 tree law. We study it over different logical systems and compare the results we obtain to already known… (More)

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)

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)

Consider a balanced non triangular two-color Pólya-Eggenberger urn process, assumed to be large which means that the ratio σ of the replacement matrix eigenvalues satisfies 1/2 < σ < 1. The composition vector of both discrete time and continuous time models admits a drift which is carried by the principal direction of the replacement matrix. In the second… (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)

- Nicolas Ollinger, Heribert Vollmer, Nicolas Ollinger Heribert, Vollmer Lifo, Susanne Albers, Tu München +436 others
- 2016

In brief, this license authorizes each and everybody to share (to copy, distribute and transmit) the work under the following conditions, without impairing or restricting the authors' moral rights: Attribution: The work must be attributed to its authors. LIPIcs is a series of high-quality conference proceedings across all fields in informatics. LIPIcs… (More)

- Antoine Genitrini, Bernhard Gittenberger, Veronika Kraus, Cécile Mailler
- 2014

We consider a probability distribution on the set of Boolean functions in n variables which is induced by random Boolean expressions. Such an expression is a random rooted plane tree where the internal vertices are labelled with connectives And and OR and the leaves are labelled with variables or negated variables. We study limiting distribution when the… (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)

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