Abstract
The notion of rank of a finite automaton is considered. The Cerny—Pin conjecture about the length of terminal words in finite abstract automata is generalized to linear automata.
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References
J. Cerny, “Poznamka k homogennym experimentom s konecnymy automatami,” Math. Fyz. Cas. SAV,14, 208–215 (1964).
E. Pin, “Sur un cas particulier de la conjecture de Cerny,” Lect. Notes Comp. Sci.,62, 345–352 (1978).
E. Pin, “La probleme de la synchronisation et la conjecture de Cerny,” Quaderni Ric. Sci.,109, 37–48 (1981).
V. M. Glushkov, “Abstract automata theory,” UMN,16, No. 2, 1–32 (1961).
I. K. Rystsov, “Bound on the length of a nuclear word for a finite automaton,” in: Automata [in Russian], SGU, Saratov, No. 2, 43–48 (1977).
I. K. Rystsov and M. A. Spivak, “Bound on the length of the shortest word of a given rank in an automaton,” Kibernetika, No. 6, 113 (1990).
J. Cerny, A. Pirica, and B. Rosenauerova, “On directable automata,” Kybernetika,7, No. 4, 289–298 (1971).
I. K. Rystsov, “Polynomial complete problems in automata theory,” Inform. Proc. Lett,16, No. 3, 147–151 (1983).
A. A. Muchnik, “General linear automata,” Probl. Kibern., Nauka, Moscow,23, 171–208 (1970).
A. Gill, Linear Sequential Machines [Russian translation], Nauka, Moscow (1974).
D. Kfoury, “Synchronizing sequences for probabilistic automata,” Stud. Appl. Math.,49, No. 1, 101–103 (1970).
M. Paterson, “Unsolvability in 3 × 3 matrices,” Stud. Appl. Math.,49, No. 1, 104–107 (1970).
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Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 3–10, May–June, 1992.
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Rystsov, I.K. Rank of a finite automaton. Cybern Syst Anal 28, 323–328 (1992). https://doi.org/10.1007/BF01125412
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DOI: https://doi.org/10.1007/BF01125412