Bi-resolving graph homomorphisms and extensions of bi-closing codes

Details Bi-resolving graph homomorphisms and extensions of bi-closing codes Bi-resolving graph homomorphisms and extensions of bi-closing codes

2009-04-20

arxiv.org/abs/0904.3042v2

Mathematics

Dynamical Systems

9 pages, 1 figure; v2) compactified. Final version to appear in Acta Appl. Math., special issue dedicated to K. H. Kim

Scientific paper

Given two graphs G and H, there is a bi-resolving (or bi-covering) graph homomorphism from G to H if and only if their adjacency matrices satisfy certain matrix relations. We investigate the bi-covering extensions of bi-resolving homomorphisms and give several sufficient conditions for a bi-resolving homomorphism to have a bi-covering extension with an irreducible domain. Using these results, we prove that a bi-closing code between subshifts can be extended to an n-to-1 code between irreducible shifts of finite type for all large n.

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