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GATE | GATE-CS-2003 | Question 53
  • Last Updated : 31 Oct, 2018

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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