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

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Abstract

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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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. U1804150, 62073124, 61973175).

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Authors and Affiliations

  1. College of Information Engineering, Henan University of Science and Technology, Luoyang, 471023, China

    Yongyi Yan

  2. Institute of Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Daizhan Cheng

  3. School of Mathematics, Shandong University, Jinan, 250100, China

    Jun-E. Feng

  4. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China

    Haitao Li

  5. College of Agricultural Equipment Engineering, Henan University of Science and Technology, Luoyang, 471023, China

    Jumei Yue

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  1. Yongyi Yan
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  5. Jumei Yue
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Yan, Y., Cheng, D., Feng, JE. et al. Survey on applications of algebraic state space theory of logical systems to finite state machines. Sci. China Inf. Sci. 66, 111201 (2023). https://doi.org/10.1007/s11432-022-3538-4

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