  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.
