Randomness number generation plays a key role in network, information security and IT applications. In this paper, a permutation and complementary algorithm is proposed to use vector complementary and permuta-tion ope...Randomness number generation plays a key role in network, information security and IT applications. In this paper, a permutation and complementary algorithm is proposed to use vector complementary and permuta-tion operations to extend n-variable Logic function space from 22n functions to 22n * 2n! configurations for variant logic framework. Each configuration contains 2n functions can be shown in a 22n-1*22n-1 matrix. A set of visual results can be represented by their symmetric properties in W, F and C codes respec-tively to provide the essential support on the variant logic framework.展开更多
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 permuta...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^(2n)×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.展开更多
文摘Randomness number generation plays a key role in network, information security and IT applications. In this paper, a permutation and complementary algorithm is proposed to use vector complementary and permuta-tion operations to extend n-variable Logic function space from 22n functions to 22n * 2n! configurations for variant logic framework. Each configuration contains 2n functions can be shown in a 22n-1*22n-1 matrix. A set of visual results can be represented by their symmetric properties in W, F and C codes respec-tively to provide the essential support on the variant logic framework.
基金This work was supported in part by Information Security Professional Education System Constructions from Yunnan University,and Yunnan Education Organization and Writing Environment in Conjugate Systems Kunming Ltd.Co.
文摘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^(2n)×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.
