A Deterministic Linear Bounded Automaton (LBA) is a single-tape TM that is not allowed to move its head past the right end of the input (but it can read and write on the portion of the tape that originally contained the input).

Show the following:

A. It is decidable whether a Deterministic LBA M accepts an input w. Hint: An instantaneous description (ID) of a TM is the current state, the current position of the head, and the current contents of the tape. Give an upper bound on the number distinct ID's to argue how long you need to run the machine before it either halts or must be in an infinite loop.

B. Part A defined a deterministic LBA to make the problem easier. In general, a LBA is defined to be non-deterministic. Generalize your construction for Part A to this case