GATE | GATE-CS-2003 | Question 53

A single tape Turing Machine M has two states q0 and q1, of which q0 is the starting state. The tape alphabet of M is {0, 1, B} and its input alphabet is {0, 1}. The symbol B is the blank symbol used to indicate end of an input string. The transition function of M is described in the following table

	0	1	B
q0	q1, 1, R	q1, 1, R	Halt
q1	q1, 1, R	q0, 1, L	q0, B, L

The table is interpreted as illustrated below.
The entry (q1, 1, R) in row q0 and column 1 signifies that if M is in state q0 and reads 1 on the current tape square, then it writes 1 on the same tape square, moves its tape head one position to the right and transitions to state q1.

Which of the following statements is true about M ?
(A) M does not halt on any string in (0 + 1)+
(B) M does not halt on any string in (00 + 1)*
(C) M halts on all string ending in a 0
(D) M halts on all string ending in a 1


Answer: (A)

Explanation:
Whenever B is given as a input, turing machine halts. This implies epsilon is only accepted when B occurs as an input.

In positive closure, epsilon is not present. So, Turing machine never halts in case of (0+1)⁺.


Thus, option (A) is correct.


Please comment below if you find anything wrong in the above post.

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