Tests for Multiple Linear Conglutinations of Variables in Boolean Functions

摘要

Let a conglutination of variables in Boolean functions be a substitution of some function depending on these variables instead of them. The conglutination is multiple if there are several blocks of conglutinated variables. In this work it is shown that the Shannon function of the length of the detecting test for multiple linear conglutinations is asymptotically equal to L~(detect)(n) ～ n~2 /2 and that the Shannon function of the length of diagnostic test for multiple linear conglutinations is equal to L~(diagn)(n) = 2~n.