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Semi-tensor product of matrices approach to reachability of finite automata with application to language recognition

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Abstract

This paper investigates the transition function and the reachability conditions of finite automata by using a semi-tensor product of matrices, which is a new powerful matrix analysis tool. The states and input symbols are first expressed in vector forms, then the transition function is described in an algebraic form. Using this algebraic representation, a sufficient and necessary condition of the reachability of any two states is proposed, based on which an algorithm is developed for discovering all the paths from one state to another. Furthermore, a mechanism is established to recognize the language acceptable by a finite automaton. Finally, illustrative examples show that the results/algorithms presented in this paper are suitable for both deterministic finite automata (DFA) and nondeterministic finite automata (NFA).

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Authors and Affiliations

  1. College of Computer and Control Engineering, Nankai University, Tianjin, 300071, China

    Yongyi Yan, Zengqiang Chen & Zhongxin Liu

  2. College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Zengqiang Chen

Authors
  1. Yongyi Yan
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  2. Zengqiang Chen
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  3. Zhongxin Liu
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Additional information

Yongyi Yan received his BS and MS degrees in mathematics from Luoyang Normal University and Xidian University in 2005 and 2008, respectively, and is currently pursuing his PhD in control theory and engineering at Nankai University, Tianjin, China. His current research interests are in the fields of modeling and optimization of complex systems, fuzzy control, and intelligent predictive control.

Zengqiang Chen received his BS degree in mathematics, and his MS, and PhD degrees in control theory and engineering from Nankai University in 1987, 1990, and 1997, respectively. He is currently a professor of control theory and engineering of Nankai University, and deputy director of the Institute of Robotics and Information Automation. His current research interests include the fields of intelligent predictive control, chaotic systems and complex dynamic networks, and multi-agent system control.

Zhongxin Liu received his BE degree in computer science and PhD degree in control theory and engineering from Nankai University in 1997 and 2002, respectively. He is currently a professor of control theory and engineering of Nankai University, Tianjin, China. His current research interests include multiagent systems, complex and dynamic networks, computer control and management.

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Yan, Y., Chen, Z. & Liu, Z. Semi-tensor product of matrices approach to reachability of finite automata with application to language recognition. Front. Comput. Sci. 8, 948–957 (2014). https://doi.org/10.1007/s11704-014-3425-y

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  • DOI: https://doi.org/10.1007/s11704-014-3425-y

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