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

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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

Self-Triggered Set Stabilization of Boolean Control Networks and Its Applications

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State-feedback set stabilization of logical control networks with state-dependent delay

自动化学报（英文版） 2024年第7期 1631页

作者： Rong Zhao jun-e feng Dawei Zhang

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Science China(Information Sciences) 2021年第6期64卷 233-235页

作者： Yating ZHeNG Haitao LI jun-e feng School of Mathematics Shandong University School of Mathematics and Statistics Shandong Normal University

Dear editor,As an important mathematical model for the elucidation,analysis, and control of gene regulatory networks(GRNs),logical networks have attracted considerable attention from scientists in numerous fields of study. From a mathematical point of view, a logical network is parameter-free; thus, it can be utilized to reconstruct relatively large-scale *** studying logical networks, stabilization is highly critical as it has been widely used in maintaining human health and treating diseases [1, 2].

关键词： State-feedback set stabilization of logical control networks with state-dependent delay

Recent advances on disturbance decoupling of Boolean control networks

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Control Theory and Technology 2023年第2期21卷 259-262页

作者： Yiliang Li jun-e feng Yingzhe Jia School of Mathematics Shandong UniversityJinan 250100ShandongChina College of electrical and Information engineering Hunan UniversityChangsha 410012HunanChina

Boolean networks(BNs)introduced by Kauffman in[1]are of great significance in the description of gene interactions/evolutions in genetic regulatory *** regulation of genes can be achieved by adding external inputs int... 详细信息

关键词： Boolean adding disturbance

Further results on dynamic-algebraic Boolean control networks

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Science China(Information Sciences) 2019年第1期62卷 177-190页

作者： Sen WANG jun-e feng Yongyuan YU Jianli ZHAO School of Mathematics Shandong University School of Mathematical Science Liaocheng University

Restricted coordinate transformation, controllability, observability and topological structures of dynamic-algebraic Boolean control networks are investigated under an assumption. Specifically, given the input-state at some point, assume that the subsequent state is certain or does not exist. First, the system can be expressed in a new form after numbering the elements in admissible set. Then, restricted coordinate transformation is raised, which allows the dimension of new coordinate frame to be different from that of the original one. The system after restricted coordinate transformation is derived in the proposed ***, three types of incidence matrices are constructed and the results of controllability, observability and topological structures are obtained. Finally, two practical examples are shown to demonstrate the theory in this paper.

关键词： controllability dynamic-algebraic Boolean control network fixed point and cycle observability restricted coordinate transformation

Data set approach for solving logical equations

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Science China(Information Sciences) 2020年第6期63卷 235-237页

作者： Sen WANG jun-e feng Yongyuan YU Xinhong WANG School of Mathematics Shandong University School of Information Science and engineering University of Jinan

Dear editor,Since Kauffman built a Boolean network model to simulate the interaction of genes in 1969 [1],Boolean networks have been used to describe relationships of cells, proteins, DNA and RNA in biological systems [2–5]. In virtue of semi-tensor product (STP), an algebraic framework was developed to analyze Boolean networks [6, 7].Logical equations arise when some variables are

关键词： Data set approach for solving logical equations

A minimum adequate set of multi-valued logic

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Control Theory and Technology 2021年第4期19卷 425-429页

作者： Daizhan Cheng jun-e feng Jianli Zhao Shihua Fu Research Center of Semi-tensor Product of Matrices:Theory and Applications Liaocheng UniversityLiaochengChina Key Laboratory of Systems and Control AMSSChinese Academy of SciencesBeijing 100190China School of Mathematics Shandong UniversityJinanChina

An adequate set of k-valued logic is provided,which contains only two *** is also proved that this adequate set is of minimum size。

关键词： k-valued logic Normal form Adequate set(ADS) Structure matrix of logical functions Semi-tensor product of matrices

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

Fault detectability of Boolean control networks via nonaugmented methods

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Science China(Information Sciences) 2023年第12期66卷 94-106页

作者： Rong ZHAO Caixia WANG Yongyuan YU jun-e feng School of Mathematics Shandong University

This study is concerned with the fault detectability of Boolean control networks(BCNs) by two nonaugmented methods. Firstly, the equivalent system-based approach is considered, and the equivalence of BCNs is applied to analyze weak active fault detectability. Further, an iterative matrix set-based approach is proposed, by which, several novel criteria for strong and weak active fault detectability are ***, effective algorithms are designed to check strong and weak active fault detectability and generate all feasible input sequences with the minimum length. In comparison, our results reduce the computational complexity dramatically than the existing studies.

关键词： Boolean control network fault detectability equivalent system nonaugmented method semitensor product