Let
X
0
X_{0}
,
X
X
be mixing one-sided subshifts of finite type such that
X
0
⊆
X
X_{0}\subseteq X
. We show a necessary and sufficient condition for the existence of mixing Markov shifts
Y
0
Y_{0}
,
Y
Y
,
Y
0
⊆
Y
Y_{0}\subseteq Y
, and a conjugacy
π
:
Y
→
X
\pi : Y\to X
with
π
(
Y
0
)
=
X
0
\pi (Y_{0})=X_{0}
, such that the sets of letters appearing in both systems are the same, more precisely,
L
1
(
Y
0
)
=
L
1
(
Y
)
L_{1}(Y_{0})=L_{1}(Y)
.