Shift Spaces, S-gap Shifts, and S-limited Shifts

An S-gap Shift is a shift space over the alphabet {0,1} where S is a subset of the natural numbers and any bi-infinite word in X(S) must have some number of 0s in S between every consecutive pair of 1s. Here, I discuss S-gap shifts and a generalization of them referred to as (S,S\u27)-gap shifts. Then, I propose a generalization of (S,S\u27)-gap shifts to an alphabet of any (finite) size, which I call as S-limited shifts