Abstract
A software system for the growth analysis of Mealy automata during iterations is discussed. The mathematical basis of the system is described. The main difficulties arising during the analysis are studied. The structure and software implementation of the system are described.
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References
R. I. Grigorchuk, “On semigroups with reductions in power growth,” Mat. Zametki, 43, No. 3, 305–319 (1988).
F. Gécseg, Products of Automata, Springer-Verlag, Berlin etc. (1986).
S. V. Alyoshin, “Finite automata and the Burnside problem on periodic groups,” Mat. Zametki, 11, No. 3, 319–328 (1972).
R. Grigorchuk and A. Zuk, “The lamplighter group as a group generated by a 2-state automaton, and its spectrum,” Geometriae Dedicata, 87, No. 1–3, 209–244 (2001).
I. I. Reznikov and V. I. Sushchanskii, “Mealy automata of intermediate growth with two states over a two-letter alphabet,” Mat. Zametki, 72, No. 1, 102–117 (2002).
V. M. Glushkov, “An abstract theory of automata,” UMN, 16, No. 5, 3–62 (1961).
V. B. Kudryavtsev, S. V. Alyoshin, and A. S. Podkolzin, Elements of the Theory of Automata [in Russian], Izd. MGU, Moscow (1978).
G. Birkhoff and T. C. Bartee, Modern Applied Algebra, McGraw-Hill, New York (1970).
I. I. Reznikov, “Mealy automata with two states over a two-element alphabet that generate a free semigroup,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauk, No. 3, 58–65 (2001).
R. I. Grigorchuk, V. V. Nekrashevich, and V. I. Sushchanskii, “Automata, dynamic systems, and groups,” Tr. Mat. In-ta im. V. A. Steklova, 231, 134–214 (2000).
I. Reznykov, “On 2-state Mealy automata of polynomial growth,” Algebra and Discrete Mathematics, No. 4, 66–85 (2003).
J. Hopcroft, “An n log n algorithm for minimizing states in a finite automaton,” Th. Mach. Comput., Proc. Int. Symp., Haifa (1971), pp. 189–196.
D. Gries, “Describing an algorithm by Hopcroft,” Acta Informatica, 2, 97–109 (1973).
L. Bartholdi, I. Reznykov, and V. Sushchanskii, “The smallest Mealy automaton of intermediate growth,” J. Algebra, 295, Issue 2, 387–414 (2006).
G. Hardy and S. Ramanujan, “Asymptotic formulae in combinatory analysis,” Proc. London Math. Soc., 17, No. 2, 75–115 (1918).
G. E. Andrews, The Theory of Partitions, Addison-Wesley Publ. Co., London-Amsterdam-Sydney-Tokio (1976).
I. Reznykov, “On composite and non-monotonic growth functions of Mealy automata,” Math. Studii, 22, No. 2, 202–214 (2004).
The GAP Group. GAP — Groups, Algorithms, and Programming, Version 4.2, Aachen, St. Andrews (1999) (http://www.gap-system.org/).
J. J. Cannon and C. Playoust, “An introduction to algebraic programming in Magma,” in: School of Math. and Stat., Sydney, Univ of Sydney (1996) (http://magma.maths.usyd.edu.au/).
I. I. Reznikov and V. I. Sushchanskii, “Growth functions of automata with two states over a two-element alphabet,” Dop. NAN Ukrainy, No. 2, 76–81 (2002).
D. A. Pospelov, Logic-Linguistic Models in Control Systems [in Russian], Energoatomizdat, Moscow (1981).
C. J. Date, An Introduction to Database Systems, Addison-Wesley, New York (1995).
Microsoft Windows DNA 2000 — The Platform for Building the Business Internet, A Microsoft Corp. White Paper, Dec. 1 (1999) (http://www.microsoft.com/technet/archive/itsolutions/intranet/build/dna2k.mspx).
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Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 125–141, March–April 2006.
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Reznikov, I.I., Sushchanskii, V.I. A software system for growth analysis of mealy automata. Cybern Syst Anal 42, 265–276 (2006). https://doi.org/10.1007/s10559-006-0062-y
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DOI: https://doi.org/10.1007/s10559-006-0062-y