Opinion evolution based on cellular automata rules in small world networks

In this paper, we apply cellular automata rules, which can be given by a truth table, to human memory. We design each memory as a tracking survey mode that keeps the most recent three opinions. Each cellular automata rule, as a personal mechanism, gives the final ruling in one time period based on the data stored in one＇s memory. The key focus of the paper is to research the evolution of people＇s attitudes to the same question. Based on a great deal of empirical observations from computer simulations, all the rules can be classified into 20 groups. We highlight the fact that the phenomenon shown by some rules belonging to the same group will be altered within several steps by other rules in different groups. It is truly amazing that, compared with the last hundreds of presidential voting in America, the eras of important events in America＇s history coincide with the simulation results obtained by our model.

Infimum Properties Differ in the Weak Truth-table Degrees and the Turing Degrees

We prove that there are non-recursive r.e.sets A and C with A<T C such that for every set F(?)T A,C∩F≡w(?).

An Extended Approach for Generating Unitary Matrices for Quantum Circuits

In this paper,we do research on generating unitary matrices for quantum circuits automatically.We consider that quantum circuits are divided into six types,and the unitary operator expressions for each type are offered.Based on this,we propose an algorithm for computing the circuit unitary matrices in detail.Then,for quantum logic circuits composed of quantum logic gates,a faster method to compute unitary matrices of quantum circuits with truth table is introduced as a supplement.Finally,we apply the proposed algorithm to different reversible benchmark circuits based on NCT library(including NOT gate,Controlled-NOT gate,Toffoli gate)and generalized Toffoli(GT)library and provide our experimental results.

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

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.

An algorithm for identifying symmetric variables based on the order eigenvalue matrix

To simplify the process for identifying 12 types of symmetric variables in Boolean functions, we propose a new symmetry detection algorithm based on minterm expansion or the truth table. First, the order eigenvalue matrix based on a truth table is defined according to the symmetry definition of a logic variable. By analyzing the constraint conditions of the order eigenvalue matrix for 12 types of symmetric variables, an algorithm is proposed for identifying symmetric variables of the Boolean function. This algorithm can be applied to identify the symmetric variables of Boolean functions with or without don't-care terms. The proposed method avoids the restriction by the number of logic variables of the graphical method, spectral coefficient methods, and AND-XOR expansion coefficient methods, and solves the problem of completeness in the fast computation method. The algorithm has been implemented in C language and tested on MCNC91 benchmarks. The application results show that, compared with the traditional methods, the new algorithm is an optimal detection method in terms of the applicability of the number of logic variables, the Boolean function including don't-care terms, detection type, and complexity of the identification process.