Full Text:   <4914>

Summary:  <455>

CLC number: TP13

On-line Access: 2024-08-27

Received: 2023-10-17

Revision Accepted: 2024-05-08

Crosschecked: 2022-02-23

Cited: 0

Clicked: 2712

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Yongyi Yan

https://orcid.org/0000-0002-7181-5894

He DENG

https://orcid.org/0000-0002-9646-578X

-   Go to

Article info.
Open peer comments

Frontiers of Information Technology & Electronic Engineering  2022 Vol.23 No.8 P.1239-1246

http://doi.org/10.1631/FITEE.2100561


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


Author(s):  He DENG, Yongyi YAN, Zengqiang CHEN

Affiliation(s):  College of Information Engineering, Henan University of Science and Technology, Luoyang 471000, China; more

Corresponding email(s):   yyyan@mail.nankai.edu.cn

Key Words:  Logical systems, Finite-valued systems, Semi-tensor product of matrices, Finite state machines, Matrix approaches


He DENG, Yongyi YAN, Zengqiang CHEN. A matrix-based static approach to analysis of finite state machines[J]. Frontiers of Information Technology & Electronic Engineering, 2022, 23(8): 1239-1246.

@article{title="A matrix-based static approach to analysis of finite state machines",
author="He DENG, Yongyi YAN, Zengqiang CHEN",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="23",
number="8",
pages="1239-1246",
year="2022",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.2100561"
}

%0 Journal Article
%T A matrix-based static approach to analysis of finite state machines
%A He DENG
%A Yongyi YAN
%A Zengqiang CHEN
%J Frontiers of Information Technology & Electronic Engineering
%V 23
%N 8
%P 1239-1246
%@ 2095-9184
%D 2022
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.2100561

TY - JOUR
T1 - A matrix-based static approach to analysis of finite state machines
A1 - He DENG
A1 - Yongyi YAN
A1 - Zengqiang CHEN
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 23
IS - 8
SP - 1239
EP - 1246
%@ 2095-9184
Y1 - 2022
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.2100561


Abstract: 
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 analysis. In 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 approaches. Based on the static approach, we reexamine the issues of closed-loop detection and controllability for deterministic finite state machines. In addition, we propose controllable equivalent form and minimal controllable equivalent form concepts and give corresponding algorithms.

一种基于矩阵的有限状态机静态分析方法

邓鹤1,闫永义1,陈增强2
1河南科技大学信息工程学院,中国洛阳市,471000
2南开大学人工智能学院,中国天津市,300071
摘要:在有限状态机研究领域,传统矩阵法首先构造状态转移矩阵,然后利用状态转移矩阵的幂来表示系统动态转移过程。这一过程是有限状态机系统分析的基石。本文提出一种基于矩阵的静态方法。该方法从拓扑结构的视角审视有限状态机,而非传统动态转移过程的视角,因此能够避免现有方法中存在的"维度爆炸"问题。基于这种静态方法,本文重新分析确定有限状态机的闭环检测与可控性问题。此外,我们提出可控等价型与最小可控等价型概念,并给出相关算法。

关键词:逻辑系统;有限值系统;矩阵的半张量积;有限状态机;矩阵方法

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1]Chen ZQ, Zhou YR, Zhang ZP, et al., 2020. Semi-tensor product of matrices approach to the problem of fault detection for discrete event systems (DESs). IEEE Trans Circ Syst II Expr Briefs, 67(12):3098-3102.

[2]Cheng DZ, Qi HS, 2010. A linear representation of dynamics of Boolean networks. IEEE Trans Autom Contr, 55(10):2251-2258.

[3]Han XG, Chen ZQ, Liu ZX, et al., 2018. The detection and stabilisation of limit cycle for deterministic finite automata. Int J Contr, 91(4):874-886.

[4]Lu JQ, Li HT, Liu Y, et al., 2017. Survey on semi-tensor product method with its applications in logical networks and other finite-valued systems. IET Contr Theory Appl, 11(13):2040-2047.

[5]Lu JQ, Sun LJ, Liu Y, et al., 2018. Stabilization of Boolean control networks under aperiodic sampled-data control. SIAM J Contr Optim, 56(6):4385-4404.

[6]Xu Q, Zhang ZP, Yan YY, et al., 2021. Security and privacy with K-step opacity for finite automata via a novel algebraic approach. Trans Inst Meas Contr, 43(16):3606-3614.

[7]Xu XR, Hong YG, 2013a. Matrix approach to model matching of asynchronous sequential machines. IEEE Trans Autom Contr, 58(11):2974-2979.

[8]Xu XR, Hong YG, 2013b. Observability analysis and observer design for finite automata via matrix approach. IET Contr Theory Appl, 7(12):1609-1615.

[9]Yan YY, Chen ZQ, Liu ZX, 2014. Semi-tensor product of matrices approach to reachability of finite automata with application to language recognition. Front Comput Sci, 8(6):948-957.

[10]Yan YY, Deng H, Chen ZQ, 2021. A new look at the critical observability of finite state machines from an algebraic viewpoint. Asian J Contr, early access.

[11]Yan YY, Yue JM, Chen ZQ, 2022. Observed data-based model construction of finite state machines using exponential representation of LMs. IEEE Trans Circ Syst II Expr Briefs, 69(2):434-438.

[12]Yue JM, Yan YY, Chen ZQ, 2019. Language acceptability of finite automata based on theory of semi-tensor product of matrices. Asian J Contr, 21(6):2634-2643.

[13]Zhu R, Chen ZQ, Zhang JL, et al., 2022. Strategy optimization of weighted networked evolutionary games with switched topologies and threshold. Knowl-Based Syst, 235:107644.

[14]Zhu SM, Feng JE, Sun LY, 2021. Matrix expression of Owen values. Asian J Contr, early access.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE