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Analysis and synthesis of abstract automata. (English. Russian original) Zbl 1257.68098
J. Math. Sci., New York 169, No. 4, 481-532 (2010); translation from Fundam. Prikl. Mat. 15, No. 4, 101-175 (2009).
Summary: This review contains some final results of research in the area of analysis and synthesis of finite automata by their behavior.

MSC:
68Q45 Formal languages and automata
68-02 Research exposition (monographs, survey articles) pertaining to computer science
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[1] A. V. Aho, J. E. Hopcroft and J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading (1974). · Zbl 0326.68005
[2] A. Bhattacharyya, Checking Experiments on Sequential Machines, Wiley, New Delhi (1989). · Zbl 0825.68458
[3] A. M. Bogomolov, A. S. Barashko, and I. S. Grunskii, Experiments on Automata [in Russian], Naukova Dumka, Kiev (1973).
[4] A. M. Bogomolov, I. S. Grunskii, and D. V. Speranskii, Control and Transformations of Discrete Automata [in Russian], Naukova Dumka, Kiev (1975).
[5] A. M. Bogomolov and V. N. Salii, Algebraic Foundations of Discrete System Theory [in Russian], Nauka, Moscow (1997).
[6] S. A. Bogomolov, On Reconstruction of Automata by Their Traces [in Russian], Candidate’s Dissertation in Physics and Mathematics, Moscow (1986).
[7] S. Yu. Borodai, ”Conditional and unconditional experiments on classes of realisations of nondeterministic automata,” in: Abstr. XI Intern. Conf. on Problems of Theoretical Cybernetics [in Russian], Ulyanovsk (1996), pp. 27–28.
[8] S. Yu. Borodai, Experiments in Effectively Determined Classes of Automata [in Russian], Candidate’s Dissertation in Physics and Mathematics, Saratov (1997).
[9] W. Brauer, Automatentheorie. Eine Einf”uhrung in die Theorie endlicher Automaten, Teubner, Stuttgart (1984).
[10] V. A. Buevich, N. G. Kalandarishvili, and A. A. Tal, ”Description of a finite automaton by means of a finite set of input-output sequences,” Autom. Remote Control, No. 199-107 (1970), · Zbl 0208.02105
[11] P. M. Cohn, Universal Algebra, Harper & Row, New York (1965). · Zbl 0141.01002
[12] N. V. Evtushenko, A. V. Lebedev and A. F. Petrenko, ”On checking experiments with nondeterministic automata,” Avtomat. Vychisl. Tekhn., 6, 81–85 (1991).
[13] N. V. Evtushenko and A. Yu. Matrosova, ”On synthesis of control-capable automata networks,” Teknn. Diagnost., 3, 143–152 (1991).
[14] N. V. Evtushenko and A. F. Petrenko, ”On checking capabilities of multiple experiments,” Avtomat. Vychisl. Tekhn., 3, 9–14 (1989).
[15] N. V. Evtushenko and A. F. Petrenko, ”A method of constructing checking experiments for an arbitrary nondeterministic automaton,” Avtomat. Vychisl. Tekhn., 5, 73–76 (1990).
[16] A. Gill, Introduction to the Theory of Finite-State Machines, McGraw-Hill, New York (1962). · Zbl 0158.25801
[17] V. M. Glushkov, ”The abstract theory of automata,” Russ. Math. Surv., 16, No. 5, 1–53 (1961). · Zbl 0104.35404 · doi:10.1070/RM1961v016n05ABEH004112
[18] I. S. Grunskii, ”Identification of control systems of automata type,” in: Proc. ICIM’98 [in Russian], Taganrog (1998), pp. 107–109.
[19] I. S. Grunskii, Analysis of the Behavior of Finite Automata [in Russian], Izd. Lugansk. Gos. Ped. Univ., Lugansk (2003). · Zbl 0374.94034
[20] I. S. Grunskii and V. A. Kozlovskii, Synthesis and Identification of Automata [in Russian], Naukova Dumka, Kiev (2004). · Zbl 1257.68098
[21] I. S. Grunskii, V. A. Kozlovskii, and O. M. Kopytova, ”Representations of automata and analysis of attacks on cryptosystems,” Iskusstv. Intellekt, 4, 764–775 (2004).
[22] I. S. Grunskii, V. A. Kozlovskii, and G. G. Ponomarenko, Representations of Finite Automata by Fragments of Behavior [in Russian], Naukova Dumka, Kiev (1990).
[23] I. S. Grunskii and I. I. Maksimenko, Experiments with Marked Automata [in Russian], Preprint 96.02 Inst. Appl. Math. Mech. Nat. Acad. Sci. Ukraine, Donetsk (1998). · Zbl 0966.68104
[24] I. S. Grunskii and I. I. Maksimenko, ”On recognition of deterministic automata determined by nondeterministic automata,” in: Proc. III Intern. Conf. ”Discrete Models in Control System Theory,” Krasnovidovo [in Russian], Moscow (1998), pp. 23–29.
[25] I. S. Grunskii and I. I. Maksimenko, ”On experiments with automata in the absence of an upper bound on the number of states,” Cybernet. Systems Anal., 35, 563–571 (1999). · Zbl 0966.68104 · doi:10.1007/BF02835853
[26] F. Harary, Graph Theory, Addison-Wesley, Reading (1969).
[27] F. C. Hennie, ”Fault detecting experiments for sequential circuits,” in: Proc. 5th Annual Symp. on Switching Circuit Theory and Logical Design, Princeton Univ., Princeton (1964), pp. 95–110.
[28] N. N. Ivanov, G. I. Mikhailov, V. V. Rudnev and A. A. Tal, Finite Automata: Equivalence and Behavior [in Russian], Nauka, Moscow (1984).
[29] Z. Kohavi, Switching and Finite Automata Theory, McGraw-Hill, New York (1970). · Zbl 0206.47701
[30] E. K. Kornoushenko, Diagnosis of Discrete Dynamic Systems by Accumulated Information [in Russian], Doctoral Dissertation in Techn. Sci., Moscow (1992). · Zbl 0810.93001
[31] E. K. Kornoushenko, ”Monitoring of logic-dynamic systems based on sampled performance data,”J. Comput. System. Sci., 30, No. 6, 107–117 (1992). · Zbl 0810.93001
[32] V. A. Kozlovskii, ”On the structure of the check experiment with an automaton,” Kibernetika, No. 319-23 (1978). · Zbl 0395.68052
[33] V. A. Kozlovskii, On Recognition of Local Faults of an Automaton [in Russian], Candidate’s Dissertation in Physics and Mathematics, Moscow (1981).
[34] V. A. Kozlovskii, ”On the recognition of an automaton relative to a locally generated class,” Sov. Math. Dokl., 23, 626–628 (1981). · Zbl 0541.68034
[35] V. A. Kozlovskii, ”On the complexity of analyzing experiments for checking local faults of an automaton,” in: Proc. of the Int. Conf. on FCT’87, Lect. Notes Comp. Sci., Vol. 278, Springer, Berlin (1987), pp. 259–262.
[36] V. A. Kozlovskii, ”Local faults of an automaton and their detection,” Mat. Vopr. Kibern., 3, 167–186 (1991). · Zbl 0825.68224
[37] V. A. Kozlovskii, ”Representations of group automata,” Cybernet. Systems Anal., 32, 168–172 (1996). · Zbl 0887.68072 · doi:10.1007/BF02366529
[38] V. A. Kozlovskii and O. M. Kopytova, ”Representations of automata relative to m-dense classes,” in: Proc. VIII Intern. Seminar ”Discrete Mathematics and Applications,” Moscow State Univ. [in Russian], Moscow (2004), pp. 277–280.
[39] S. A. Kryvyi and L. E. Matveeva, ”Formal methods for the analysis of the properties of systems,” Cybernet. Systems Anal., 39, 174–191 (2003). · Zbl 1099.68658 · doi:10.1023/A:1024783021463
[40] V. B. Kudryavtsev, S. V. Aleshin, and A. S. Podkolzin, Introduction to Automata [in Russian], Nauka, Moscow (1985). · Zbl 0604.68058
[41] A. B. Kuznetsov and B. A. Trakhtenbrot, ”Investigation of partially recursive operators by means of the Baire space theory,” Dokl. Akad. Nauk SSSR, 105, 897–900 (1955).
[42] B. D. Lukyanov, ”Distinguishing and control experiments with nondeterministic automata,” Cybernet. Systems Anal., 31, 691–696 (1995). · Zbl 0854.68064 · doi:10.1007/BF02366317
[43] B. D. Lukyanov, ”Deterministic realizations of nondeterministic automata,” Cybernet. Systems Anal., 32, 493–504 (1996). · Zbl 0880.68093 · doi:10.1007/BF02366771
[44] I. I. Maksimenko, ”Recognition in effectively determined classes of automata,” Tr. Inst. Prikl. Mat. Mekh. Nac. Akad. Nauk Ukrainy 2, 115–123 (1998).
[45] I. I. Maksimenko, ”Experiments in a class of realizations of nondeterministic automata,” Dokl. NAN Ukrainy, 7, 95–99 (1999). · Zbl 0958.68083
[46] I. I. Maksimenko, Experiments in Finitely Defined Metric Spaces of Automata [in Russian], Candidate’s Dissertation in Physics and Mathematics, Saratov (2000).
[47] E. F. Moore, ”Gedanken-experiments on sequential machines,” Ann. Math. Stud., 34, 129–153 (1956).
[48] P. P. Parkhomenko, ed., Fundamentals of Technical Diagnosis [in Russian], Energiya, Moscow (1976).
[49] A. F. Petrenko, ”Experiments with protocol entities,” Avtomat. Vychisl. Tekhn., 1, 16–21 (1987).
[50] A. F. Petrenko, Automaton Methods of Analysis of the Consistency of Interaction Facilities in Open Networks [in Russian], Doctoral Dissertation in Techn. Sci., Riga (1988).
[51] A. F. Petrenko, N. Yevtushenko, and R. Dssouli, Grey-Box FSM-Based Testing Strategies, Dept. Publ. 991. Dept. IRO, Univ. de Montreal (1994).
[52] D. K. Pradhan, ed., Fault-Tolerant Computing: Theory and Techniques, Vol. 1, Prentice Hall, Upper Saddle River (1986).
[53] L. A. Skornyakov, ed., General Algebra, Vol. 1 [in Russian], Nauka, Moscow (1990). · Zbl 0751.00002
[54] M. A. Spivak, ”On the synthesis of a finite automaton in terms of its set of experiments,” Kibernetika, 5, 15–20 (1969).
[55] B. A. Trakhtenbrot and Ya. M. Barzdin, Finite Automata. Behavior and Synthesis, North-Holland, Amsterdam (1973).
[56] M. P. Vasilevskii, ”The detection of the disrepair of automata,” Kibernetika, No. 493–108 (1973).
[57] V. N. Zakharov, D. A. Pospelov, and V. E. Khazatskii, Control Systems: Specification, Design, Implementation [in Russian], Energiya, Moscow (1972).
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