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And/or tree probabilities of Boolean functions

Abstract : We consider two probability distributions on Boolean functions defined in terms of their representations by $\texttt{and/or}$ trees (or formulas). The relationships between them, and connections with the complexity of the function, are studied. New and improved bounds on these probabilities are given for a wide class of functions, with special attention being paid to the constant function $\textit{True}$ and read-once functions in a fixed number of variables.
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https://hal.inria.fr/hal-01184027
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Danièle Gardy, Alan Woods. And/or tree probabilities of Boolean functions. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. pp.139-146. ⟨hal-01184027⟩

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