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Discussiones Mathematicae General Algebra and Applications 25(1) (2005) 103-118
DOI: https://doi.org/10.7151/dmgaa.1094

SEMIGROUPS DEFINED BY AUTOMATON EXTENSION MAPPINGS

Mirosław Osys

Silesian University of Technology
Institute of Mathematics,
Kaszubska 23, 44-100 Gliwice, Poland
e-mail: Miroslaw.Osys@polsl.pl

Abstract

We study semigroups generated by the restrictions of automaton extension (see, e.g., [3]) and give a characterization of automaton extensions that generate finite semigroups.

Keywords: automaton mapping, Mealy automaton, semigroup.

2000 Mathematics Subject Classification: 68Q70, 68Q45, 20M35.

References

[1]	K. Culik, II, Construction of the Automaton Mapping, (Russian), Apl. Mat. 10 (1965), 459-468.
[2]	S. Eilenberg, Automata, Languages and Machines, Volume A, Academic Press, New York 1974.
[3]	V.M. Glushkov, Abstract theory of automata, (Russian), Uspehi Mat. Nauk 16 no. 5 (101), (1961), 3-62.
[4]	R.I. Grigorchuk, V.V. Nekrashevich and V.I. Sushchanskii, Automata,Dynamical Systems, and Groups, Proc. Steklov Inst. Math. 231 (2000), 128-203.
[5]	B. Mikolajczak et al. (eds.) , Algebraic and Structural Automata Theory, Annals of Discrete Mathematics, vol. 44, North-Holland Publ. Co., Amsterdam 1991.
[6]	M. Osys, Automaton extensions of mappings on the set of words defined by finite Mealy automata, Algebra Discrete Math., to appear (preprint 2005).
[7]	M. Osys, Automaton extensions of transformations of free monoid over finite alphabet (Polish), Zeszyty Nauk. Politech. Śląskiej, Seria Math.-Fiz., no. 91, (2004).
[8]	G.N. Raney, Sequential functions, J. Assoc. Comput. Math. 5 (1958), 177-180.
[9]	Y. Sheng, Regular languages, p. 41-110 in: Handbook of Formal Languages, vol. 1, Springer-Verlag, Berlin 1997.

Received 12 May 2005
Revised 19 July 2005