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Survey on applications of algebraic state space theory of logical systems to finite state machines

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Science China(Information Sciences) 2023年第1期66卷 5-24页

作者： Yongyi YAN Daizhan CHENG Jun-E FENG Haitao LI jumei yue College of Information Engineering Henan University of Science and Technology Institute of Systems Science Chinese Academy of Sciences School of Mathematics Shandong University School of Mathematics and Statistics Shandong Normal University College of Agricultural Equipment Engineering Henan University of Science and Technology

Algebraic state space theory(ASST) of logical systems, developed based on the semi-tensor product(STP) which is a new matrix analysis tool built in recent ten years, provides an algebraic analysis approach for many fields of science, such as logical dynamical systems, finite-valued systems, discrete event dynamic systems, and networked game systems. This study focuses on comprehensively surveying the applications of the ASST method to the field of finite state machines(FSMs). Some necessary preliminaries on the method are first reviewed. Then the applications of the method in the FSM field are reviewed, including deterministic FSMs, nondeterministic FSMs, probabilistic FSMs, networked FSMs, and controlled and combined FSMs. In addition, other applications related to both STP and FSMs are surveyed, such as the application of FSM to Boolean control networks and the application of graph theory to FSMs. Finally, some potential research directions with respect to the ASST method in the FSM field are predicted.

关键词： Boolean control network Boolean network finite state machine learning system semi-tensor product (STP) ASST

Algebraic state space approach to model and control combined automata

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Frontiers of Computer Science 2017年第5期11卷 874-886页

作者： Yongyi YAN Zengqiang CHEN jumei yue College of Information Engineering Henan University of Science and Technology Luoyang 471023 China College of Computer and Control Engineering Nankai University Tianjin 300071 China College of Agricultural Engineering Henan University of Science and Technology Luoyang 471003 China

A new modeling tool, algebraic state space approach to logical dynamic systems, which is developed recently based on the theory of semi-tensor product of matrices （STP）, is applied to the automata field. Using the STE this paper investigates the modeling and controlling problems of combined automata constructed in the ways of parallel, serial and feedback. By representing the states, input and output symbols in vector forms, the transition and output functions are expressed as algebraic equations of the states and inputs. Based on such algebraic descriptions, the control problems of combined automata, including output control and state control, are considered, and two necessary and sufficient conditions are presented for the controllability, by which two algorithms are established to find out all the control strings that make a combined automaton go to a target state or produce a desired output. The results are quite different from existing methods and provide a new angle and means to understand and analyze the dynamics of combined automata.

关键词： automata composition controllability algebraic state space approach semi-tensor product

State space optimization of finite state machines from the viewpoint of control theory

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Frontiers of Information Technology & Electronic Engineering 2021年第12期22卷 1598-1609页

作者： jumei yue Yongyi YAN Zengqiang CHEN He DENG College of Agricultural Equipment Engineering Henan University of Science and TechnologyLuoyang 471003China College of Information Engineering Henan University of Science and TechnologyLuoyang 471003China College of Artificial Intelligence Nankai UniversityTianjin 300071China

Motivated by the inconvenience or even inability to explain the mathematics of the state space optimization of finite state machines(FSMs)in most existing results,we consider the problem by viewing FSMs as logical dynamic *** ideas from the concept of equilibrium points of dynamic systems in control theory,the concepts of t-equivalent states and t-source equivalent states are *** on the state transition dynamic equations of FSMs proposed in recent years,several mathematical formulations of t-equivalent states and t-source equivalent states are *** can be analogized to the necessary and sufficient conditions of equilibrium points of dynamic systems in control theory and thus give a mathematical explanation of the optimization *** these mathematical formulations,two methods are designed to find all the t-equivalent states and t-source equivalent states of ***,two ways of reducing the state space of FSMs are *** can be implemented without computers but with only pen and paper in a mathematical *** addition,an open question is raised which can further improve these methods into unattended ***,the correctness and effectiveness of the proposed methods are verified by a practical language model.

关键词： Finite state machines Finite-valued systems Logical systems Logical networks Semi-tensor product of matrices Space optimization

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Three matrix conditions for the reduction of finite automata based on the theory of semi-tensor product of matrices

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Science China(Information Sciences) 2020年第2期63卷 227-229页

作者： jumei yue Yongyi YAN Zengqiang CHEN College of Agricultural Engineering Henan University of Science and Technology College of Information Engineering Henan University of Science and Technology College of Computer and Control Engineering Nankai University

Dear editor,Reduction of finite automata (FA) is of great importance because of its practical applications in engineering; for example the memory space of hardware realization grows exponentially with the number of states of FSMs. Existing results for reducing FA can roughly be classified into four categories:merging of states [1], refining of the state

关键词： STP Sr Three matrix conditions for the reduction of finite automata based on the theory of semi-tensor product of matrices

Algebraic criteria for finite automata understanding of regular language

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Frontiers of Computer Science 2019年第5期13卷 1148-1150页

作者： Yongyi YAN jumei yue Zhumu FU Zengqiang CHEN School of Information Engineering Henan University of Science and Technology Henan 471003 China College of Agricultural Equipment Engineering Henan University of Science and Technology Henan 471003 China College of Artificial Intelligence Nankai University Tianjin 300071 China

1 Introduction and main contributions Finite automata are dynamical systems with discrete inputs and outputs, which belong to the domain of logical systems and have a wide range of applications. In engineering, due to the excellent hardware qualities of simple structure, low power consumption and low electromagnetic noise, etc., finite automata are used in avionics and nuclear engineering, where the environment is bad and require strict safety. In science, finite automata serve as one of the main molding tools for discrete event dynamic systems (DEDS)(others are Petri nets, Markov chains and queuing networks, etc.). Studying DEDS is one of the major ways to study the cyber physical systems (CPS) which is the core content of Industry 4.0.

关键词： Algebraic criteria finite automata regular language

Logical Approach to Livelock and Deadlock of Deterministic Finite State Machines: Modelling and Finding

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Logical Approach to Livelock and Deadlock of Deterministic F...

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作者： Yongyi Yan jumei yue Zengqiang Chen College of Information Engineering Henan University of Science and Technology College of Agricultural Equipment Engineering Henan University of Science and Technology College of Artificial Intelligence Nankai University

Inspired by the connections between logical dynamic systems and continuous variable dynamic systems, this paper addresses the modelling and finding of the livelock and deadlock of deterministic finite state machines（DFSMs） from a logical viewpoint, where a DFSM is viewed as a logical system by treating the input string and current state of a DFSM as the input signal and state of a logical system, respectively. A difference equation-like model is proposed to formulate the dynamics of DFSMs and the behavior of deadlock and livelock of DFSMs. Based on the model and by generalizing livelock and deadlock as a loop structure, a unified discriminate criterion is established by which whether a DFSM contains livelock or dead lock can be judged easily. Further,an algorithm is designed for finding all the livelocks and deadlocks for a given DFSM.

关键词： Logical systems logical networks finite-valued systems semi-tensor product of matrices finite state machines logical blocking

Graph Models for Security Monitoring of Streets and Balance Communication of WSNs

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Graph Models for Security Monitoring of Streets and Balance ...

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作者： Yongyi YAN jumei yue He DENG College of Information Engineering Henan University of Science and Technology College of Agricultural Equipment Engineering Henan University of Science and Technology

The concepts of k-degree and k-balance control sets of graphs are abstracted from some real-world problems such as the location of cameras for saving resources in street security monitoring and the arrangement of major sensors for balancing load in wireless sensor networks. Then using a new matrix analysis tool, semi-tensor product of matrices（STP） developed in recent years, such two kinds of control sets are formulated by establishing a necessary and sufficient conditions that determine whether or not a vertex subset of a graph is a k-degree control set, and a necessary condition that facilitates finding k-balance control sets of a graph. Finally the effectiveness of the idea and the correctness of the results are verified by studying security monitoring of a street.

关键词： logical systems logical networks finite-valued systems semi-tensor product of matrices

Finite Input and Given Time Critical Observabilities of Finite State Machines Based on the Semi-tensor Product of Matrices

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Finite Input and Given Time Critical Observabilities of Fini...

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作者： He Deng Yongyi Yan jumei yue College of Information Engineering Henan University of Science and Technology College of Agricultural Equipment Engineering Henan University of Science and Technology

The notion of safety in safety-critical applications can be represented by the concept of critical observability. The traditional concept of critical observability refers to possibility of detecting if the current state of a nondeterministic finite state machine（NFSM）belongs to a so-called critical set for any input and any initial state. In practice, the input is always of finite length and we may only care about the state of an FSM at a given time step or the inverse problem that how to find all possible inputs moving the FSM to a critical state of interest. Thus, we propose two new concepts about critical observability, critical observability with finite input and critical observability at a given time step, to cope with these two cases. From the view of algebraic model resulting from the theory of semi-tensor product（STP）, we propose corresponding algebraic criteria and algorithms. They are based on matrix operation, which means that they naturally avoid the design of critical observers and can be solved efficiently by computers.

关键词： Logical systems logical networks finite-valued systems finite state machines critical observability semi-tensor product of matrices

STP Approach to Formulate k-Externally Stable Sets of Graphs

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STP Approach to Formulate k-Externally Stable Sets of Graphs

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作者： jumei yue Yongyi Yan Zengqiang Chen College of Agricultural Equipment Engineering Henan University of Science and Technology College of Information Engineering Henan University of Science and Technology College of Artificial Intelligence Nankai University

In this paper the structure of graphs in terms of k-externally stable set（k-ESS） is investigated based on a new matrix product, called semi-tensor product of matrices. By defining an eigenvector and an eigenvalue of node subset of a graph, three necessary and sufficient conditions of k-ESS are proposed in a matrix form. Using these conditions, the concepts of k-ESS matrix are introduced. The k-ESS matrix provides the complete information of the corresponding structures of a graph. Further, an algorithm is designed to find all the structures of a graph by conducting a series of matrix operation. The proposed method and results may offer a new way to investigate the problems related to graph structures in the field of network systems.

关键词： STP Semi-tensor product of matrices k-ESS logical systems finite-valued systems matrix method