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Matrix expression and reachability analysis of finite automata

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Abstract

In this paper, we propose a matrix-based approach for finite automata and then study the reachability conditions. Both the deterministic and nondeterministic automata are expressed in matrix forms, and the necessary and sufficient conditions on reachability are given using semitensor product of matrices. Our results show that the matrix expression provides an effective computational way for the reachability analysis of finite automata.

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Authors and Affiliations

  1. Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Xiangru Xu & Yiguang Hong

Authors
  1. Xiangru Xu
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  2. Yiguang Hong
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Corresponding author

Correspondence to Xiangru Xu.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 61174071).

Xiangru XU received his B.S. degree in Applied Mathematics from Beijing Normal University in 2009. Currently, he is a Ph.D. candidate of Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China. His research interests include automata theory and multi-agent systems.

Yiguang HONG received his B.S. and M.S. degrees from Peking University in 1987 and 1990, respectively, and Ph.D. degree from Chinese Academy of Sciences (CAS) in 1993. He is currently a professor in Academy of Mathematics and Systems Science, CAS. He is serving as Deputy Editor-in-Chief of Acta Automatica Sinca, and Associate Editors for several journals including IEEE TAC. His current research interests include nonlinear control, multi-agent systems, and complex systems.

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Xu, X., Hong, Y. Matrix expression and reachability analysis of finite automata. J. Control Theory Appl. 10, 210–215 (2012). https://doi.org/10.1007/s11768-012-1178-4

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  • DOI: https://doi.org/10.1007/s11768-012-1178-4

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