Volume 15, No 6, 2008, P. 4857
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 abovementioned 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
email: mathcyb@cs.msu.su
