Complexity and Probability of Some Boolean Formulas
Combinatorics, Probability and Computing
Combinatorics, Probability and Computing
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The present paper deals with the problem of analyzing the value of a random Boolean expression. The expressions are constructed of Boolean operations and constants chosen independently at random with given probabilities. The dependence between the expression value probability and the constants' probabilities is investigated for different sets of operations. The asymptotic behavior of this dependence is given by a probability function, explicitly obtained through analysis of generating functions for expressions. Special attention is given to the case of binary Boolean operations. The paper demonstrates some probability function properties and their connection with the properties of Boolean operations used in random expressions.