Completely Separating Systems

The author introduces a definition of binary codes that are redundant completely separating systems, with the aim of employing them for antirace and simultaneously noise-stable state assignment for asynchronous discrete automata. The limits of the parameters of these codes are determined. Concatenated codes with the above properties are constructed on the basis of Reed–Solomon codes. It is shown that the requirement of noise stability does not conflict with the property of monotonicity of the logical functions of the combination unit of the automaton, which obtains upon state assignment by completely separating systems that are not redundant.