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

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, discre...

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Bibliographic Details
Published in:Science China. Information sciences Vol. 66; no. 1; p. 111201
Main Authors: Yan, Yongyi, Cheng, Daizhan, Feng, Jun-E., Li, Haitao, Yue, Jumei
Format: Journal Article
Language:English
Published: Beijing Science China Press 01.01.2023
Springer Nature B.V
Subjects:
Algebra
Computer Science
Discrete event systems
Dynamical systems
Fields (mathematics)
Finite state machines
Graph theory
Information Systems and Communication Service
Matrix methods
Review
Tensors
semi-tensor product (STP)
learning system
Boolean network
finite state machine
ASST
Boolean control network
ISSN:1674-733X, 1869-1919
Online Access:Get full text
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Summary: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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ISSN:1674-733X
1869-1919
DOI:10.1007/s11432-022-3538-4