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

作     者：Yongyi YAN Daizhan CHENG Jun-E FENG Haitao LI Jumei YUE 

作者机构：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 

出 版 物：《Science China(Information Sciences)》 (中国科学:信息科学(英文版))

年 卷 期：2023年第66卷第1期

页      面：5-24页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0811[工学-控制科学与工程] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant Nos. U1804150  62073124  61973175) 

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

摘      要：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.