Hostname: page-component-cc8bf7c57-8cnds Total loading time: 0 Render date: 2024-12-11T11:06:03.488Z Has data issue: false hasContentIssue false

Some Algebraic Properties of Machine Poset of Infinite Words

Published online by Cambridge University Press:  03 June 2008

Aleksandrs Belovs*
Affiliation:
Department of Mathematics, University of Latvia, Raiņa bulvāris 19, Rīga, Latvia; stiboh@inbox.lv
Get access

Abstract

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.

Type
Research Article
Copyright
© EDP Sciences, 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

J. Berstel and J. Karhumäki, Combinatorics on Words – A Tutorial. TUCS Technical Report (No 530, June) (2003).
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.
J. Dassow, Completeness Problems in the Structural Theory of Automata. Mathematical Research (Band 7), Akademie–Verlag, Berlin (1981).
B.A. Davey and H.A. Priestley, Introduction to Lattices and Order. Cambridge University Press (2002).
Fine, N.J. and Wilf, H.S., Uniqueness theorem for periodic functions. Proc. Amer. Math. Soc. 16 (1965) 109114. CrossRef
J. Hartmanis and R.E. Stearns, Algebraic Structure Theory of Sequential Machines. Prentice–Hall, Inc., Englewood Cliffs, New Jersey (1966).
M. Lothaire, Combinatorics on Words. Encyclopedia of Mathematics and its Applications, Vol. 17, Addison–Wesley, Reading, Massachusetts (1983).
M. Lothaire, Algebraic Combinatorics on Words. Encyclopedia of Mathematics and its Applications, Vol. 90, Cambridge University Press, Cambridge (2002).
A. Luca and S. Varricchio, Finiteness and Regularity in Semigroups and Formal Languages. Springer-Verlag, Berlin, Heidelberg (1999).
McNaughton, R., Testing and generating infinite sequences by a finite automaton. Inform. Control 9 (1966) 521530. CrossRef
Mealy, G.H., A method for synthesizing sequential circuits. Bell System Tech. J. 34 (1955) 10451079. CrossRef
D. Perrin and J.-E. Pin, Infinite words: automata, semigroups, logic and games. Pure Appl. Math. 141 (2004).
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).
H. Rogers, Theory of recursive functions and effective computability. McGraw-Hill Book Company (1967).
Sacks, G.E., The recursively enumerable degrees are dense. Ann. Math. 80 (1964) 300312. CrossRef
S. Seshu, Mathematical models for sequential machines. IRE Mat. Convent, Rec. 7 (1959) 4–16.
Wagner, K., On ω-regular sets. Informatics and Control 43 (1979) 123177. CrossRef
V.B. Kudryavcev, S.V. Aleshin and A.S. Podkolzin, An introduction to the theory of automata. Moskva Nauka (1985) (Russian).
A.A. Kurmit, Sequential decomposition of finite automata. Riga Zinatne (1982) (Russian).
B.A. Trahtenbrot and Ya.M. Barzdin, Finite automata, behaviour and synthesis. Moskva Nauka (1970) (Russian).