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

被引：0
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作者：
Yongyi Yan
Daizhan Cheng
Jun-E. Feng
Haitao Li
Jumei Yue
机构：
[1] Henan University of Science and Technology,College of Information Engineering
[2] Chinese Academy of Sciences,Institute of Systems Science
[3] Shandong University,School of Mathematics
[4] Shandong Normal University,School of Mathematics and Statistics
[5] Henan University of Science and Technology,College of Agricultural Equipment Engineering
来源：
Science China Information Sciences | 2023年 / 66卷
关键词：
Boolean control network; Boolean network; finite state machine; learning system; semi-tensor product (STP); ASST;
D O I：
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中图分类号：
学科分类号：
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.
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