Recognizing the nonrepeating property in an arbitrary basis

Two classical problems are considered: recognizing the properties of a Boolean function given a column of its values and constructing a diagnostic test. The problems are investigated for nonrepeating functions in an arbitrary basis B. For the first problem, the decomposition method is applied to prove linear complexity of the corresponding sequential circuits; for the second problem we derive the order of the Shannon functions for a number of bases, in particular, for the basis of all functions of four variables. __________ Translated from Prikladnaya Matematika i Informatika, No. 23, pp. 67–84, 2006.