The relation between tree size complexity and probability for boolean functions generated by uniform random trees

Veronika Daxner; Antoine Genitrini; Bernhard Gittenberger; Cecile Mailler

doi:10.2298/AADM160715015D

The relation between tree size complexity and probability for boolean functions generated by uniform random trees

Veronika Daxner, Antoine Genitrini, Bernhard Gittenberger, Cecile Mailler

Research output: Contribution to journal › Article › peer-review

1 Citation (SciVal)

Abstract

An associative Boolean tree is a plane rooted tree whose internal nodes are labelled by and or or and whose leaves are labelled by literals taken from a fixed set of variables and their negations. We study the distribution induced on the set of Boolean functions by the uniform distribution on the set of associative trees of a large fixed size, where the size of a tree is defined as the number of its nodes. Using analytic combinatorics, we prove a relation between the probability of a given function and its tree size complexity.

Original language	English
Pages (from-to)	408-446
Number of pages	39
Journal	Applicable Analysis and Discrete Mathematics
Volume	10
Issue number	2
DOIs	https://doi.org/10.2298/AADM160715015D
Publication status	Published - 1 Jan 2016

Keywords

Analytic combinatorics
Boolean functions
Probability distribution
Random Boolean formulas
Tree size complexity

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.2298/AADM160715015D

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AU - Genitrini, Antoine

AU - Gittenberger, Bernhard

AU - Mailler, Cecile

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N2 - An associative Boolean tree is a plane rooted tree whose internal nodes are labelled by and or or and whose leaves are labelled by literals taken from a fixed set of variables and their negations. We study the distribution induced on the set of Boolean functions by the uniform distribution on the set of associative trees of a large fixed size, where the size of a tree is defined as the number of its nodes. Using analytic combinatorics, we prove a relation between the probability of a given function and its tree size complexity.

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KW - Analytic combinatorics

KW - Boolean functions

KW - Probability distribution

KW - Random Boolean formulas

KW - Tree size complexity

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The relation between tree size complexity and probability for boolean functions generated by uniform random trees

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Keywords

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Emergence of Condensation in Stochastic Systems

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The relation between tree size complexity and probability for boolean functions generated by uniform random trees

Abstract

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ASJC Scopus subject areas

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Emergence of Condensation in Stochastic Systems

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