A note on minimal covers for sofic systems

Boyle, Mike; Kitchens, Bruce; Marcus, Brian

doi:10.1090/S0002-9939-1985-0806078-7

A note on minimal covers for sofic systems
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by Mike Boyle, Bruce Kitchens and Brian Marcus

Proc. Amer. Math. Soc. 95 (1985), 403-411

DOI: https://doi.org/10.1090/S0002-9939-1985-0806078-7

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Abstract:

We characterize the sofic systems which have minimal subshift-of-finite-type covers and derive some consequences.

References

Roy L. Adler and Brian Marcus, Topological entropy and equivalence of dynamical systems, Mem. Amer. Math. Soc. 20 (1979), no. 219, iv+84. MR 533691, DOI 10.1090/memo/0219
I. Csiszár and J. Komlós, On the equivalence of two models of finite-state noiseless channels from the point of view of the output, Proc. Colloquium on Information Theory (Debrecen, 1967) János Bolyai Math. Soc., Budapest, 1968, pp. 129–133. MR 0252108
Ethan M. Coven and Michael E. Paul, Endomorphisms of irreducible subshifts of finite type, Math. Systems Theory 8 (1974/75), no. 2, 167–175. MR 383378, DOI 10.1007/BF01762187
Ethan M. Coven and Michael E. Paul, Sofic systems, Israel J. Math. 20 (1975), no. 2, 165–177. MR 383379, DOI 10.1007/BF02757884
R. Fischer, Graphs and symbolic dynamics, Topics in information theory (Second Colloq., Keszthely, 1975) Colloq. Math. Soc. János Bolyai, Vol. 16, North-Holland, Amsterdam, 1977, pp. 229–244. MR 0466486
Roland Fischer, Sofic systems and graphs, Monatsh. Math. 80 (1975), no. 3, 179–186. MR 407235, DOI 10.1007/BF01319913
G. A. Hedlund, Endomorphisms and automorphisms of the shift dynamical system, Math. Systems Theory 3 (1969), 320–375. MR 259881, DOI 10.1007/BF01691062
Wolfgang Krieger, On sofic systems. I, Israel J. Math. 48 (1984), no. 4, 305–330. MR 776312, DOI 10.1007/BF02760631
Brian Marcus, Sofic systems and encoding data, IEEE Trans. Inform. Theory 31 (1985), no. 3, 366–377. MR 794434, DOI 10.1109/TIT.1985.1057037
Masakazu Nasu, Constant-to-one and onto global maps of homomorphisms between strongly connected graphs, Ergodic Theory Dynam. Systems 3 (1983), no. 3, 387–413. MR 741394, DOI 10.1017/S0143385700002042
Masakazu Nasu, An invariant for bounded-to-one factor maps between transitive sofic subshifts, Ergodic Theory Dynam. Systems 5 (1985), no. 1, 89–105. MR 782790, DOI 10.1017/S0143385700002777
Benjamin Weiss, Subshifts of finite type and sofic systems, Monatsh. Math. 77 (1973), 462–474. MR 340556, DOI 10.1007/BF01295322