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Structure of weakly invertible semi-input-memory finite automata with delay 1. (English) Zbl 1012.68104

Summary: Semi-input-memory finite automata, a kind of finite automata introduced by the first author of this paper for studying error propagation, are a generalization of input-memory finite automata by appending an autonomous finite automaton component. In this paper, we give a characterization of the structure of weakly invertible semi-input-memory finite automata with delay 1, in which the state graph of each autonomous finite automaton is a cycle. From a result on mutual invertibility of finite automata obtained by the authors recently, it leads to a characterization of the structure of feedforward inverse finite automata with delay 1.

MSC:

68Q45 Formal languages and automata
Full Text: DOI

References:

[1] Huffman D A. Canonical forms for information-lossless finite-state logical machines.IRE Trans. Circuit Theory, 1959, CT-6 (special supplement): 41–59. · Zbl 0166.26802
[2] Kurmit A A. Information Lossless Automata of Finite Order. John Wiley, New York, 1974. · Zbl 0363.94053
[3] Tao J. Invertible linear finite automata.Scientia Sinica, 1973, 16(4): 565–581. · Zbl 0341.94027
[4] Tao R J. Invertibility of Finite Automata. Science Press, Beijing, 1979. (in Chinese) · Zbl 0609.68041
[5] Tao R J. Relationship between bounded error propagation and feedforward invertibility.Kexue Tongbao, 1982, 27(6): 680–682. · Zbl 0583.68027
[6] Tao R J. Some results on the structure of feedforward inverses.Scientia Sinica, Ser. A, 1984, 27(2): 157–162. · Zbl 0527.68033
[7] Tao R J. Invertibility of linear finite automata over a ring. InICALP’88, Automata, Languages and Programming, Lecture Notes in Computer Science 317, Springer-Verlag, Berlin, 1988, pp.489–501.
[8] Tao R J, Chen S H. Some properties on the structure of invertible and inverse finite automata with delay r.Chinese J. Computers, 1980, 3(4): 289–297. (in Chinese)
[9] Tao R J, Chen S H. A necessary condition on invertibility of finite automata.Science in China, Ser. E, 1997, 40(6): 637–643. · Zbl 0895.68090
[10] Tao R J, Chen S H. Constructing finite automata with invertibility by transformation method.J. Computer Science and Technology, 2000, 15(1): 10–26. · Zbl 1044.94535 · doi:10.1007/BF02951923
[11] Tao R J, Chen S H. Input-trees of finite automata and application to cryptanalysis.J. Computer Science and Technology, 2000, 15(4): 305–325. · Zbl 0976.94024 · doi:10.1007/BF02948867
[12] Chen S H. On the structure of inverses of a weakly invertible linear finite automaton.Chinese J. Computers, 1981, 4(6): 409–419. (in Chinese)
[13] Chen S H. On the structure of finite automata of whichM’ is an (weak) inverse with delayr.J. Computer Science and Technology, 1986, 1(2): 54–59. · Zbl 0605.68043 · doi:10.1007/BF02943272
[14] Chen S H. On the structure of (weak) inverses of an (weakly) invertible finite automaton.J. Computer Science and Technology, 1986, 1(3): 92–100. · doi:10.1007/BF02979465
[15] Chen S H, Tao R J. The structure of weak inverses of a finite automaton with bounded error propagation.Kexue Tongbao, 1987, 32(10): 713–714; full paper inAdvances in Chinese Computer Science, Vol.1, World Scientific, Singapore, 1988, pp. 205–211.
[16] Chen S H, Tao R J. Invertibility of quasi-linear finite automata. InAdvances in Cryptology – CHINACRYPT’92, Science Press, Beijing, 1992, pp.77–86. (in Chinese)
[17] Zhu X J. On the structure of binary feedforward inverses with delay 2.J. Computer Science and Technology, 1989, 4(2): 163–171. · Zbl 0688.68052 · doi:10.1007/BF02943364
[18] Bao F. On the structure ofn-ary feedforward inverses with delay 1 [Thesis]. Institute of Software, Chinese Academy of Sciences, 1986. (in Chinese)
[19] Bao F. Limited error-propagation, self-synchronization and finite input memory FSMs as weak inverses InAdvances in Chinese Computer Science, Vol.3, World Scientific, Singapore, 1991, pp.1–24.
[20] Bao F. Composition and decomposition of weakly invertible finite automata.Science in China, Ser. A, 1993, 23(7): 759–766 (in Chinese)
[21] Bao F. Two results about the decomposition of delay step of weakly invertible finite automata.Chinese J. Computers, 1993, 16(8): 629–632. (in Chinese)
[22] Gao X, Bao F. Decomposition of binary weakly invertible finite automata.Chinese J. Computers, 1994, 17(5): 330–337. (in Chinese)
[23] Zhou S Y. On the weakly invertibility of type I Abelian FGHSS.Chinese J. Computers, 1982, 5(3): 221–222. (in Chinese)
[24] Lü S Z. Some results on the invertibility of linear finite automata over a ring.Chinese J. Computers, 1991, 14(8): 570–578. (in Chinese)
[25] Dai Z D, Ye D F. Weak invertibility of nonlinear finite automata over commutative rings.Chinese Science Bulletin, 1995, 40(15): 1357–1360. (in Chinese)
[26] Wang H.R a Rb transformation of compound finite automata over commutative rings.J. Computer Science and Technology, 1997, 12(1): 40–48. · Zbl 0865.68079 · doi:10.1007/BF02943143
[27] Wang H. On weak invertibility of linear finite automata.Chinese J. Computers, 1997, 20(11): 1003–1008 (in Chinese)
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