Entropy bounds for multi-word perturbations of subshifts

Given a subshift S of finite type and a finite set S of finite words, let S(S) denote the subshift of S that avoids S. We establish a general criterion under which we can bound the entropy perturbation h(S) - h(S(S)) from above. As an application, we prove that this entropy difference tends to zero with a sequence of such sets S1, S2, ... under various assumptions on the S-i.