2014/07/02 by Antoine Genitrini, Bernhard Gittenberger, Genitrini, Antoine +5
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algorithms and Data Compression #Combinatorics (math.CO) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Topological and Geometric Data Analysis #math.CO #math.PR #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1407.0501
openalex publication_date 2014/07/02 · arxiv created 2015/09/25 · arxiv updated 2015/09/28 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28
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 tree size tends to infinity and derive a relation between the tree size complexity and the probability of a function. This is done by first expressing trees representing a particular function as expansions of minimal trees representing this function and then computing the probabilities by means of combinatorial counting arguments relying on generating functions and singularity analysis.