Bent functions and random Boolean formulas (Q1910518)

The author's previous three papers [Discrete Math. 83, 95--103 (1990; Zbl 0703.06006), Eur. J. Comb. 15, 407--410 (1994; Zbl 0797.94011), Comb. Probab. Comput. 7, No. 4, 451--463 (1998; Zbl 0927.68041)] are referred to and the degree of a connective is analysed. For asymptotic estimate of an arbitrary degree connective the Fourier transform is used. All the results of the paper are only asymptotic. It is proved, that the bent functions achieve asymptotically the minimal probability of occurring among all Boolean functions. At the same time, the linear functions achieve asymptotically the maximal probability. This paper presents 36 definitions, theorems and lemmas. It needs to be compared with the theory of Boolean functions [\textit{I. Wegener}, The complexity of Boolean functions. Stuttgart: B. G. Teubner (1987; Zbl 0623.94018)]. The bibliography contains 11 references.