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Consider the TM where tape alphabet is {a, b, blank} with transitions (q0, a) → (q0, a, R), (q0, blank) → (q0, blank, R), (q0, b) → (qh, b) where qh is a halting state. Select all inputs on which the TM loops.1 pointeaaaaabbbbaba

Question

Consider the TM where tape alphabet is {a, b, blank} with transitions (q0, a) → (q0, a, R), (q0, blank) → (q0, blank, R), (q0, b) → (qh, b) where qh is a halting state. Select all inputs on which the TM loops.1 pointeaaaaabbbbaba

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Solution

The Turing Machine (TM) described has the following transitions:

  1. (q0, a) → (q0, a, R): If the machine is in state q0 and reads an 'a', it stays in state q0, writes an 'a' and moves right.
  2. (q0, blank) → (q0, blank, R): If the machine is in state q0 and reads a blank, it stays in state q0, writes a blank and moves right.
  3. (q0, b) → (qh, b): If the machine is in state q0 and reads a 'b', it goes to the halting state qh and writes a 'b'.

Given these transitions, the TM will loop on any input that does not contain a 'b'. This is because the only transition to the halting state qh is triggered by reading a 'b'. If the TM never reads a 'b', it will continue to loop indefinitely in state q0, moving right and rewriting the same symbol it reads.

Therefore, the TM will loop on any input string composed only of 'a' and/or blank symbols.

This problem has been solved

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