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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1122, author = {Aleksandrs Belovs and J\=anis Buls}, title = {The completely distributive lattice of machine invariant sets of infinite words}, journal = {Discussiones Mathematicae - General Algebra and Applications}, volume = {27}, year = {2007}, pages = {109-121}, zbl = {1132.06303}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1122} }
Aleksandrs Belovs; Jānis Buls. The completely distributive lattice of machine invariant sets of infinite words. Discussiones Mathematicae - General Algebra and Applications, Tome 27 (2007) pp. 109-121. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1122/
[000] [1] J. Berstel and J. Karhumäki, Combinatorics on Words - A Tutorial, Bulletin of the European Association for Theoretical Computer Science 79 (2003), 178-228. | Zbl 1169.68560
[001] [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).
[002] [3] J. Dassow, Completeness Problems in the Structural Theory of Automata, Mathematical Research (Band 7), Akademie-Verlag, Berlin 1981. | Zbl 0481.68052
[003] [4] B.A. Davey and H.A. Priestley, Introduction to Lattices and Order, Cambridge University Press, 2002. | Zbl 1002.06001
[004] [5] J.A. Goguen, L-fuzzy sets, J. Math. Anal. Appl. 8 (1967), 145-174. | Zbl 0145.24404
[005] [6] J. Hartmanis and R.E. Stearns, Algebraic Structure Theory of Sequential Machines, Prentice-Hall, Inc., Englewood Cliffs, New Jersey 1966. | Zbl 0154.41701
[006] [7] A. de Luca and S. Varricchio, Finiteness and Regularity in Semigroups and Formal Languages, Springer-Verlag, Berlin, Heidelberg 1999. | Zbl 0935.68056
[007] [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. | Zbl 0875.68657
[008] [9] D.R. Stinson, Cryptography, Theory and Practice, CRC Press 1995.
[009] [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. | Zbl 0604.68058
[010] [11] A.A. Kurmit, Posledovatel'naya dekompoziciya konechnyh avtomatov, Sequential Decomposition of Finite Automata, Riga, Zinatne (Russian) 1982. | Zbl 0558.68049
[011] [12] B.A. Trahtenbrot and Ya.M. Barzdin, Konechnye avtomaty povedenie i sintez, Finite Automata (Behaviour and Synthesis) Moskva, Nauka (Russian) 1970.
[012] [13] V.M. Fomichev, Diskretnaya matematika i kriptologiya, (Discrete Mathematics and Cryptology), Moskva, DIALOG-MIFI (Russian) 2003.