Some algebraic properties of machine poset of infinite words
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 42 (2008) no. 3, pp. 451-466.

The complexity of infinite words is considered from the point of view of a transformation with a Mealy machine that is the simplest model of a finite automaton transducer. We are mostly interested in algebraic properties of the underlying partially ordered set. Results considered with the existence of supremum, infimum, antichains, chains and density aspects are investigated.

DOI: 10.1051/ita:2008009
Classification: 03D40,  20F10
Keywords: infinite words, Mealy machine, poset, algebraic properties
@article{ITA_2008__42_3_451_0,
author = {Belovs, Aleksandrs},
title = {Some algebraic properties of machine poset of infinite words},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {451--466},
publisher = {EDP-Sciences},
volume = {42},
number = {3},
year = {2008},
doi = {10.1051/ita:2008009},
zbl = {1167.68030},
mrnumber = {2434028},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ita:2008009/}
}
TY  - JOUR
AU  - Belovs, Aleksandrs
TI  - Some algebraic properties of machine poset of infinite words
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2008
DA  - 2008///
SP  - 451
EP  - 466
VL  - 42
IS  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ita:2008009/
UR  - https://zbmath.org/?q=an%3A1167.68030
UR  - https://www.ams.org/mathscinet-getitem?mr=2434028
UR  - https://doi.org/10.1051/ita:2008009
DO  - 10.1051/ita:2008009
LA  - en
ID  - ITA_2008__42_3_451_0
ER  - 
%0 Journal Article
%A Belovs, Aleksandrs
%T Some algebraic properties of machine poset of infinite words
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2008
%P 451-466
%V 42
%N 3
%I EDP-Sciences
%U https://doi.org/10.1051/ita:2008009
%R 10.1051/ita:2008009
%G en
%F ITA_2008__42_3_451_0
Belovs, Aleksandrs. Some algebraic properties of machine poset of infinite words. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 42 (2008) no. 3, pp. 451-466. doi : 10.1051/ita:2008009. http://www.numdam.org/articles/10.1051/ita:2008009/

[1] J. Berstel and J. Karhumäki, Combinatorics on Words - A Tutorial. TUCS Technical Report (No 530, June) (2003). | MR

[2] J.R. Büchi, On a Decision Method in Restricted Second Order Arithmetic, in Proc. Internat. Congr. on Logic, Methodology and Philosophy of Science, edited by E. Nagel et al., Stanford Univ. Press, Stanford, CA (1960) 1-11. | MR

[3] J. Dassow, Completeness Problems in the Structural Theory of Automata. Mathematical Research (Band 7), Akademie-Verlag, Berlin (1981). | MR | Zbl

[4] B.A. Davey and H.A. Priestley, Introduction to Lattices and Order. Cambridge University Press (2002). | MR | Zbl

[5] N.J. Fine and H.S. Wilf, Uniqueness theorem for periodic functions. Proc. Amer. Math. Soc. 16 (1965) 109-114. | MR | Zbl

[6] J. Hartmanis and R.E. Stearns, Algebraic Structure Theory of Sequential Machines. Prentice-Hall, Inc., Englewood Cliffs, New Jersey (1966). | MR | Zbl

[7] M. Lothaire, Combinatorics on Words. Encyclopedia of Mathematics and its Applications, Vol. 17, Addison-Wesley, Reading, Massachusetts (1983). | MR | Zbl

[8] M. Lothaire, Algebraic Combinatorics on Words. Encyclopedia of Mathematics and its Applications, Vol. 90, Cambridge University Press, Cambridge (2002). | MR | Zbl

[9] A. Luca and S. Varricchio, Finiteness and Regularity in Semigroups and Formal Languages. Springer-Verlag, Berlin, Heidelberg (1999). | MR | Zbl

[10] R. Mcnaughton, Testing and generating infinite sequences by a finite automaton. Inform. Control 9 (1966) 521-530. | MR | Zbl

[11] G.H. Mealy, A method for synthesizing sequential circuits. Bell System Tech. J. 34 (1955) 1045-1079. | MR

[12] D. Perrin and J.-E. Pin, Infinite words: automata, semigroups, logic and games. Pure Appl. Math. 141 (2004). | Zbl

[13] B.I. Plotkin, I.Ja. Greenglaz and A.A. Gvaramija, Algebraic Structures in Automata and Databases Theory. World Scientific, Singapore, New Jersey, London, Hong Kong (1992). | Zbl

[14] H. Rogers, Theory of recursive functions and effective computability. McGraw-Hill Book Company (1967). | MR | Zbl

[15] G.E. Sacks, The recursively enumerable degrees are dense. Ann. Math. 80 (1964) 300-312. | MR | Zbl

[16] S. Seshu, Mathematical models for sequential machines. IRE Mat. Convent, Rec. 7 (1959) 4-16.

[17] K. Wagner, On $\omega$-regular sets. Informatics and Control 43 (1979) 123-177. | MR | Zbl

[18] V.B. Kudryavcev, S.V. Aleshin and A.S. Podkolzin, An introduction to the theory of automata. Moskva Nauka (1985) (Russian).

[19] A.A. Kurmit, Sequential decomposition of finite automata. Riga Zinatne (1982) (Russian). | MR

[20] B.A. Trahtenbrot and Ya.M. Barzdin, Finite automata, behaviour and synthesis. Moskva Nauka (1970) (Russian). | MR

Cited by Sources: