《Frontiers of Electrical and Electronic Engineering》
A framework to express variant and invariant functional spaces for binary logic
作者:
JZJ Zheng，CH Zheng
关键词:
two-dimensional (2D) organization；conjugate symmetry；cellular automata (CA)；permutation；meta-state；vector space；truth table (TT)；variant table (VT)；invariant table (IVT)；variant logic
摘要:
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 completerepresentation 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 22n脳2n! 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 electricelectronic technology and engineering, and has uses in the analysis of the stability of rule-based, dynamic binary systems such as cellular automata.
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