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Three matrix conditions for the reduction of finite automata based on the theory of semi-tensor product of matrices

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  1. 1

    Almeida J, Zeitoun M. Description and analysis of a bottom-up DFA minimization algorithm. Inf Process Lett, 2008, 107: 52–59

  2. 2

    David J. The average complexity of Moore’s state minimization algorithm is O(nloglogn). Lect Notes Comput Sci, 2010, 6281: 318–329

  3. 3

    Peeva K. Equivalence, reduction and minimization of finite automata over semirings. Theory Comput Sci, 1991, 88: 269–285

  4. 4

    Lamperti G, Scandale M. Incremental determinization and minimization of finite acyclic automata. In: Proceedings of IEEE International Conference on Systems, Man, and Cybernetics, 2013. 2250–2257

  5. 5

    Holzer M, Kutrib M. Descriptional and computational complexity of finite automata: a survey. Inf Comput, 2011, 209: 456–470

  6. 6

    Carrasco R C, Forcada M L. Incremental construction and maintenance of minimal finite-state automata. Comput Linguist, 2002, 28: 207–216

  7. 7

    Zhang ZP, Chen Z Q, Liu Z X. Modeling and reachability of probabilistic finite automata based on semitensor product of matrices. Sci China Inf Sci, 2018, 61: 129202

  8. 8

    Yue J M, Chen Z Q, Yan Y Y, et al. Solvability of k-track assignment problem: a graph approach. Control Theory Appl, 2017, 34: 457–466

  9. 9

    Cheng D Z, Qi H S, Zhao Y. An Introduction to Semi-Tensor Product of Matrices and Its Applications. Singapore: World Scientific Publishing, 2012

  10. 10

    Aho A V, Sethi R, Ullman J D. Compilers, Principles, Techniques, and Tools. Boston: Addison-Wesley Publishing Corporation, 1986

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This work was supported by National Natural Science Foundation of China (Grant Nos. U1804150, 61573199) and 2018 Henan Province Science and Technique Foundation (Grant No. 182102210045).

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Correspondence to Yongyi Yan.

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Yue, J., Yan, Y. & Chen, Z. Three matrix conditions for the reduction of finite automata based on the theory of semi-tensor product of matrices. Sci. China Inf. Sci. 63, 129203 (2020). https://doi.org/10.1007/s11432-018-9739-9

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