Summary: A language is dense if the set of all infixes (or subwords) of the language is the set of all words. Here, it is shown that it is decidable whether the language accepted by a nondeterministic Turing machine with a one-way read-only input and a reversal-bounded read/write worktape (the read/write head changes direction at most some fixed number of times) is dense.
From this, it is implied that it is also decidable for one-way reversal-bounded queue automata, one-way reversal-bounded stack automata, one-way reversal-bounded \(k\)-flip pushdown automata (machines that can “flip” their pushdowns up to \(k\) times).
However, it is undecidable for deterministic Turing machines with two one-reversal-bounded worktapes (even when the two tapes are restricted to operate as one-reversal-bounded pushdown stacks).