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On transformations of probability distributions by read-once quasigroup formulae

Abstract - We investigate distributions of values of read-once quasigroup formulae when the variables are replaced by random independent identically distributed elements of the quasigroup. For general read-once formulae of increasing complexity or depth conditions under which of the distributions of values of the formulae converge to the uniform distribution are put forward, and weaker conditions for the convergence ‘in the mean’ is proved also. This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 11-01-00508) and by the Programme of the Division of Mathematics Sciences of the Russian Academy of Sciences “Algebraic and Combinatorial Methods of Mathematical and New Generation of Information Systems” (the project “Problems of Optimal Synthesis of Control Systems”).