What kind of languages can be recognized by a restricted one-tape deterministic Turing Machine? During a lesson, our TA asked: 


  What kind of languages can be recognized by a deterministic Turing
  Machine such that we can use only a tape portion that contains the input?


My thoughts:
my Theory of Computation book says that there is a special TM called linear bounded automaton (LBA) that corresponds to a non-deterministic Turing Machine that has a limited tape. Such machine recognize Context Sensitive languages.

So if i simulate the LBA behavior starting from a deterministc TM, may I recognize "deterministic"-Context Sensitive Languages?
It's famously unknown whether deterministic and non-deterministic LBA accept the same set of languages.