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An STP look at logical blocking of finite state machines: formulation, detection, and search

Science China(Information Sciences) 2024年第10期67卷 332-342页

作者： Yongyi YAN Penglei HAO Jumei YUE Haitao LI Jun-E FENG College of Information Engineering Henan University of Science and Technology College of Agricultural Equipment Engineering Henan University of Science and Technology School of Mathematics and Statistics Shandong Normal University School of Mathematics Shandong University

The logical blocking of finite state machines(FSMs) is examined at the three levels of formulation,detection, and search from an STP viewpoint(semi-tensor product of matrices). The research idea regards an FSM as a logical system. The realizing method treats the event sequence exciting an FSM as the input signal of a logical system and treats the current states of an FSM as the states of a logical system. Based on a recently developed bilinear dynamic model of FSMs, a difference equation-like model is first proposed to describe the logical blocking. By defining a loop structure of FSMs and using the difference equation-like model, a criterion is built by which whether a given FSM is blocking can be easily judged. If it is, several algorithms are designed to find all the logical blocking of the FSM. Further, these results are extended to apply to the case of nondeterministic FSMs and, thus, to networks of FSMs. The proposed STP approach may provide a new angle for considering the problems of FSMs, and the presented results may strengthen the links between systems governed by human-designed rules and systems governed by natural laws.

关键词： semi-tensor product of matrices STP matrix approach finite-valued systems logical systems logical networks finite state machines

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

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

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第40届中国控制会议

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

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A matrix-based static approach to analysis of finite state machines

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Frontiers of Information Technology & Electronic Engineering 2022年第8期23卷 1239-1246页

作者： He DENG Yongyi YAN Zengqiang CHEN College of Information Engineering Henan University of Science and TechnologyLuoyang 471000China College of Artificial Intelligence Nankai UniversityTianjin 300071China

Traditional matrix-based approaches in the field of finite state machines construct state transition matrices,and then use the powers of the state transition matrices to represent corresponding dynamic transition processes,which are cornerstones of system *** this study,we propose a static matrix-based approach that revisits a finite state machine from its structure rather than its dynamic transition process,thus avoiding the“explosion of complexity”problem inherent in the existing *** on the static approach,we reexamine the issues of closed-loop detection and controllability for deterministic finite state *** addition,we propose controllable equivalent form and minimal controllable equivalent form concepts and give corresponding algorithms.

关键词： logical systems Finite-valued systems Semi-tensor product of matrices Finite state machines Matrix approaches

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

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

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第40届中国控制会议

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

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Observability Analysis of Composite Automata based on Algebraic State Space

Observability Analysis of Composite Automata based on Algebr...

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第三十九届中国控制会议

作者： Yingrui Zhou Zengqiang Chen Zhipeng Zhang Zhongxin Liu College of Artificial Intelligence Nankai University School of Computer Science and Engineering Tianjin University of Technology

Observability analysis of Discrete Event systems（DESs） is a significant subject. In this paper, a matrix approach to verify four kinds of observability of partial-observed composite automata is proposed. Firstly, as a class of logic dynamic systems, DESs, modeled as finite automata, can be established its algebraic structure by semi-tensor product of matrices and due to the actual needs, we focus on composite automata formed by prallel composition. Then, aiming at initial state observability and current state observability with or without input information, we construct two polynomial matrices and present four necessary and sufficient theorems to verify the corresponding observability. Besides, all results obtained in this paper are applied to a practical example: the exhaust gas recirculation system.

关键词： Observability Composite Automata Semi-tensor Product of Matrices logical systems

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

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

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第40届中国控制会议

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

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STP Approach to Formulate k-Externally Stable Sets of Graphs

STP Approach to Formulate k-Externally Stable Sets of Graphs

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第40届中国控制会议

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

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