Associative and commutative tree representations for Boolean functions

作者：Genitrini Antoine^*; Gittenberger Bernhard; Kraus Veronika; Mailler Cecile

来源：Theoretical Computer Science, 2015, 570: 70-101.

DOI：10.1016/j.tcs.2014.12.025

• Boolean functions
• Probability distribution
• Random Boolean formulas
• Random trees
• Asymptotic ratio
• Analytic combinatorics

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: non-binary or non-plane trees. These formulas satisfy the natural properties of associativity and commutativity.

• 出版日期2015-3-9