A framework to express variant and invariant functional spaces for binary logic

Abstract

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 2 2 n  2 n ! 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.

Interactive Maps on Variant Phase Spaces– From Measurements - Micro Ensembles to Ensemble Matrices on Statistical Mechanics of Particle Models

“…It is necessary to clearly describe these four modules in order to understand the measurement properties of variant construction [35]- [44]. Relevant information and supporting materials on fundamental levels of variant construction are briefly descried in Section 3.1 and the four modules are investigated in Sections 3.2 through 3.5.…”

“…The variant measurement construction is based on n-variable logic functions and N bit vectors taken as input and output results [40,43,44].…”

“…For given n 0-1 variables, a given function J and an N bit vector X, the following corollaries can be described [35]- [44]. Corollary 3.1: For n 0-1 variables, the state set contains a total of 2 n states.…”

“…Further discussion on the details of variant coding scheme has been previously published in [40,44].…”

From Local Interactive Measurements to Global Matrix Representations on Variant Construction – A Particle Model of Quantum Interactions for Double Path Experiments

“…The variant principle is based on n-variable logic functions [Zheng (2011);Zheng & Zheng (2010;2011a;; Zheng et al (2011)]. …”