Minimal presentations for irreducible sofic shifts

We re-cast a theorem of Willems (1989) in terms of symbolic dynamics. We then present a new result which characterizes when an irreducible sofic shift (i.e., constrained system) has a unique minimal irreducible presentation. >

[1]  Brian H. Marcus,et al.  Bounds on the number of states in encoder graphs for input-constrained channels , 1991, IEEE Trans. Inf. Theory.

[2]  Brian Marcus,et al.  Topological entropy and equivalence of dynamical systems , 1979 .

[3]  Brian H. Marcus,et al.  Sofic systems and encoding data , 1985, IEEE Trans. Inf. Theory.

[4]  Wolfgang Krieger On sofic systems II , 1984 .

[5]  Masakazu Nasu Constant-to-one and onto global maps of homomorphisms between strongly connected graphs , 1983 .

[6]  Roland Fischer Sofic systems and graphs , 1975 .

[7]  Danrun Huang Flow equivalence of reducible shifts of finite type , 1994, Ergodic Theory and Dynamical Systems.

[8]  Paul H. Siegel,et al.  Matched spectral-null codes for partial-response channels , 1989, IEEE Trans. Inf. Theory.

[9]  John Atkins A note on minimal covers , 1988, SGMD.

[10]  Masakazu Nasu,et al.  An invariant for bounded-to-one factor maps between transitive sofic subshifts , 1985, Ergodic Theory and Dynamical Systems.

[11]  Brian H. Marcus,et al.  Canonical Encoders for Sliding Block Decoders , 1995, SIAM J. Discret. Math..

[12]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[13]  Chris Heegard,et al.  Trellis group codes for the Gaussian channel , 1995, IEEE Trans. Inf. Theory.

[14]  Susan G. Williams Covers of non-almost-finite type sofic systems , 1988 .

[15]  Mike Boyle,et al.  A note on minimal covers for sofic systems , 1985 .

[16]  Mike Boyle,et al.  Resolving maps and the dimension group for shifts of finite type , 1987 .

[17]  B. Weiss Subshifts of finite type and sofic systems , 1973 .

[18]  Jan C. Willems,et al.  Models for Dynamics , 1989 .