Abstract
Traditional matrix-based approaches in the field of finite state machines construct state transition matrices, and then use the powers of the state transition matrices to represent corresponding dynamic transition processes, which are cornerstones of system analysis. In this study, we propose a static matrix-based approach that revisits a finite state machine from its structure rather than its dynamic transition process, thus avoiding the “explosion of complexity” problem inherent in the existing approaches. Based on the static approach, we reexamine the issues of closed-loop detection and controllability for deterministic finite state machines. In addition, we propose controllable equivalent form and minimal controllable equivalent form concepts and give corresponding algorithms.
摘要
在有限状态机研究领域, 传统矩阵法首先构造状态转移矩阵, 然后利用状态转移矩阵的幂来表示系统动态转移过程. 这一过程是有限状态机系统分析的基石. 本文提出一种基于矩阵的静态方法. 该方法从拓扑结构的视角审视有限状态机, 而非传统动态转移过程的视角, 因此能够避免现有方法中存在的“维度爆炸”问题. 基于这种静态方法, 本文重新分析确定有限状态机的闭环检测与可控性问题. 此外, 我们提出可控等价型与最小可控等价型概念, 并给出相关算法.
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He DENG conceived the concept, designed the research, and drafted the paper. Yongyi YAN and Zengqiang CHEN supervised the research, helped organize the paper, and revised and finalized the paper.
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He DENG, Yongyi YAN, and Zengqiang CHEN declare that they have no conflict of interest.
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Project supported by the National Natural Science Foundation of China (Nos. U1804150, 62073124, and 61973175)
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Deng, H., Yan, Y. & Chen, Z. A matrix-based static approach to analysis of finite state machines. Front Inform Technol Electron Eng 23, 1239–1246 (2022). https://doi.org/10.1631/FITEE.2100561
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DOI: https://doi.org/10.1631/FITEE.2100561
Key words
- Logical systems
- Finite-valued systems
- Semi-tensor product of matrices
- Finite state machines
- Matrix approaches