Volume 15, No 6, 2008, P. 48-57

UDC 519.716
S. S. Marchenkov, V. S. Fedorova
On solutions of systems of functional boolean equations

Abstract:
Solutions of systems of functional Boolean equations are considered. For each class $P_2,T_0,T_1,S,T_{01},S_{01}$ the problem of construction of functional Boolean equations systems with a fixed set of functional constants and one functional variable whose unique solution is of the concerned class is solved. For an arbitrary nonempty set $F$ of $n$-argument Boolean functions, the system of equations with functional constants $\vee$ and $\&$ is built with $F$ as the solution set. If the above-mentioned set $F$ is closed under transition to dual functions, then the corresponding system of functional Boolean equations can be constructed without functional constants at all. 
Bibl. 12.

Keywords: functional Boolean equation, closed class of Boolean functions.

Marchenkov Sergey Serafimovich ¹
Fedorova Valentina Sergeevna ¹
1. Lomonosov Moscow State University,
Vorob’evy ghory, 119992 Moscow, Russia
e-mail: mathcyb@cs.msu.su