%A Jeffrey Zhi J. ZHENG, Christian H. ZHENG,
%T A framework to express variant and invariant
functional spaces for binary logic
%0 Journal Article
%D 2010
%J Front. Electr. Electron. Eng.
%J Frontiers of Electrical and Electronic Engineering
%@ 2095-2732
%R 10.1007/s11460-010-0011-4
%P 163-172
%V 5
%N 2
%U {https://journal.hep.com.cn/fee/EN/10.1007/s11460-010-0011-4
%8 2010-06-05
%X A new framework has been developed to express variant and invariant properties of functions operating on a binary vector space. This framework allows for manipulation of dynamic logic using basic operations and permutations. Novel representations of binary functional spaces are presented. Current ideas of binary functional spaces are extended and additional conditions are added to describe new function representation schemes: F code and C code.

Sizes of the proposed functional space representation schemes were determined. It was found that the complete representation for any set of functions operating on a binary sequence of numbers is larger than previously thought. The complete representation can only be described using a structure having a space of size for any given space of functions acting on a binary sequence of length *n*. The framework, along with the proposed coding schemes provides a foundational theory of variant and invariant logic in software and electric-electronic technology and engineering, and has uses in the analysis of the stability of rule-based, dynamic binary systems such as cellular automata.