The completely distributive lattice of machine invariant sets of infinite words

Aleksandrs Belovs; Jānis Buls

Discussiones Mathematicae - General Algebra and Applications (2007)

  • Volume: 27, Issue: 1, page 109-121
  • ISSN: 1509-9415

Abstract

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We investigate the lattice of machine invariant classes. This is an infinite completely distributive lattice but it is not a Boolean lattice. The length and width of it is c. We show the subword complexity and the growth function create machine invariant classes.

How to cite

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Aleksandrs Belovs, and Jānis Buls. "The completely distributive lattice of machine invariant sets of infinite words." Discussiones Mathematicae - General Algebra and Applications 27.1 (2007): 109-121. <http://eudml.org/doc/276885>.

@article{AleksandrsBelovs2007,
abstract = {We investigate the lattice of machine invariant classes. This is an infinite completely distributive lattice but it is not a Boolean lattice. The length and width of it is c. We show the subword complexity and the growth function create machine invariant classes.},
author = {Aleksandrs Belovs, Jānis Buls},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {mealy machine; machine invariant class; completely distributive lattice; length; width; Mealy machine; lattice of machine-invariant classes; subword complexity; growth function},
language = {eng},
number = {1},
pages = {109-121},
title = {The completely distributive lattice of machine invariant sets of infinite words},
url = {http://eudml.org/doc/276885},
volume = {27},
year = {2007},
}

TY - JOUR
AU - Aleksandrs Belovs
AU - Jānis Buls
TI - The completely distributive lattice of machine invariant sets of infinite words
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2007
VL - 27
IS - 1
SP - 109
EP - 121
AB - We investigate the lattice of machine invariant classes. This is an infinite completely distributive lattice but it is not a Boolean lattice. The length and width of it is c. We show the subword complexity and the growth function create machine invariant classes.
LA - eng
KW - mealy machine; machine invariant class; completely distributive lattice; length; width; Mealy machine; lattice of machine-invariant classes; subword complexity; growth function
UR - http://eudml.org/doc/276885
ER -

References

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  1. [1] J. Berstel and J. Karhumäki, Combinatorics on Words - A Tutorial, Bulletin of the European Association for Theoretical Computer Science 79 (2003), 178-228. Zbl1169.68560
  2. [2] J. Buls, Machine Invariant Classes, p. 207-211 in: 'Proceedings of WORDS'03, 4th International Conference on Combinatorics on Words', September 10-13, 2003, Turku, Finland, Tero Harju and Juhani Karhumäki (Eds.), TUCS General Publication (No 27, August). 
  3. [3] J. Dassow, Completeness Problems in the Structural Theory of Automata, Mathematical Research (Band 7), Akademie-Verlag, Berlin 1981. Zbl0481.68052
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  8. [8] 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. Zbl0875.68657
  9. [9] D.R. Stinson, Cryptography, Theory and Practice, CRC Press 1995. 
  10. [10] V.B. Kudryavcev, S.V. Aleshin and A.S. Podkolzin, Vvedenie v teoriyu avtomatov, An Introduction to the Theory of Automata, Moskva, Nauka (Russian) 1985. Zbl0604.68058
  11. [11] A.A. Kurmit, Posledovatel'naya dekompoziciya konechnyh avtomatov, Sequential Decomposition of Finite Automata, Riga, Zinatne (Russian) 1982. Zbl0558.68049
  12. [12] B.A. Trahtenbrot and Ya.M. Barzdin, Konechnye avtomaty povedenie i sintez, Finite Automata (Behaviour and Synthesis) Moskva, Nauka (Russian) 1970. 
  13. [13] V.M. Fomichev, Diskretnaya matematika i kriptologiya, (Discrete Mathematics and Cryptology), Moskva, DIALOG-MIFI (Russian) 2003. 

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