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On the structure of a sofic shift space


Author: Klaus Thomsen
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 3557-3619
MSC (2000): Primary 37B10
DOI: https://doi.org/10.1090/S0002-9947-04-03437-3
Published electronically: January 16, 2004
MathSciNet review: 2055747
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Abstract: The structure of a sofic shift space is investigated, and Krieger's embedding theorem and Boyle's factor theorem are generalized to a large class of sofic shifts.


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  • [B] M. Boyle, Lower entropy factors of sofic systems, Ergod. Th. & Dynam. Sys. 4 (1984), 541-557. MR 85m:54014
  • [BK] M. Boyle and W. Krieger, Almost Markov and shift equivalent sofic systems, Proceedings of the Maryland Special Year in Dynamics 1986-87, Springer-Verlag, LNM 1342 (1988), 33-93. MR 89i:28007
  • [BKM] M. Boyle, B. Kitchens and B. Marcus, A note on minimal covers for sofic systems, Proc. Amer. Math. Soc. 95 (1985), 403-411. MR 87d:54068
  • [BH] F. Blanchard and G. Hansel, Systèmes codés, Theor. Computer Sci. 44 (1986), 17-49. MR 88m:68029
  • [CP] E. Coven and M. Paul, Finite procedures for sofic systems, Monats. Math. 83 (1977), 265-278. MR 57:1454
  • [FF] D. Fiebig and U. Fiebig, Covers for coded systems, in Symbolic Dynamics and Its Applications, Contemporary Mathematics 135 (ed. P. Walters), Amer. Math. Soc., Providence, 1992, pp. 139-180. MR 93e:00030
  • [FFJ] D. Fiebig, U. Fiebig, N. Jonoska, Multiplicities of covers for sofic shifts, Theor. Comp. Science 262 (2001), 349-375. MR 2002e:37011
  • [Gu] B.M. Gurevic, Topological entropy of enumerable Markov chains, Soviet Math. Dokl. 10 (1969), 911-915.
  • [J1] N. Jonoska, Sofic shifts with synchronizing presentations, Theor. Comp. Science 158 (1996), 81-115. MR 97d:68110
  • [J2] -, A conjugacy invariant for reducible sofic shifts and its semigroup characterizations, Israel J. Math. 106 (1998), 221-249. MR 99h:58056
  • [K1] W. Krieger, On the Subsystems of Topological Markov Chains, Ergod. Th. & Dynam. Sys. 2 (1982), 195-202. MR 85b:28020
  • [K2] -, On Sofic Systems I, Israel J. Math. 48 (1984), 305-330. MR 86j:54074
  • [K3] -, On Sofic Systems II, Israel J. Math. 60 (1987), 167-176. MR 89k:54098
  • [LM] D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press (1995). MR 97a:58050
  • [M1] B. Marcus, Sofic systems and encoding data, IEEE Trans. Inform. Theory 31 (1985), 366-377. MR 86m:94021
  • [M2] -, The Impact of Roy Adler's Work on Symbolic Dynamics and Applications to Data Storage, in Symbolic Dynamics and Its Applications, Contemporary Mathematics 135 (ed. P. Walters), Amer. Math. Soc., Providence, 1992, pp. 125-138. MR 93e:00030
  • [N1] M. Nasu, An invariant for bounded-to-one factor maps between transitive sofic subshifts, Ergod. Th. & Dynam. Sys. 3 (1985), 89-105. MR 86i:28030
  • [N2] -, Topological conjugacy for sofic systems and extensions of automorphisms of finite subsystems of topological Markov shifts, Proceedings of the Maryland Special Year in Dynamics 1986-87, Springer-Verlag, LNM 1342 (1988), 564-607. MR 89j:54045
  • [P] K. Petersen, Chains, entropy, coding, Ergod. Th. & Dynam. Sys. 6 (1986), 415-448. MR 88i:28040
  • [T] P. Trow, Determining presentations of sofic shifts, Theor. Comp. Science 259 (2001), 199-216. MR 2002c:37014

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Additional Information

Klaus Thomsen
Affiliation: Institut for matematiske fag, Ny Munkegade, 8000 Aarhus C, Denmark
Email: matkt@imf.au.dk

DOI: https://doi.org/10.1090/S0002-9947-04-03437-3
Received by editor(s): November 24, 2002
Received by editor(s) in revised form: April 18, 2003
Published electronically: January 16, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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