Question

Give an informal description of a deterministic Turing machine for the language L = {x ∈ {0, 1}* | x is not of the form 0w1w for w ∈ {0, 1}*}.

Answer 1

This problem is simple to evaluate using multitape deterministic Turing machine, which will accept string x by rejecting the string x if it is in the form of 0w1w and accept otherwise. The Turing machine will work as follows:-

1. On input string x, if the starting symbol is not 0 then accept because it cannot be in the form of 0w10.

2. If starting input is 0, then consume this 0, and then find the middle element of remaining string. Now if the input left on input tape is w1w then the middle element must be 1.

3. If the middle element is 0 then accept the input, otherwise copy the content of substring following middle input 1 into the second tape. Also remove the middle 1 as well as all the substring following 1 from the input tape.

4. Now check if the string on the input tape and string on second tape are same, this happen only when input is of the form 0w1w. If they are same then reject the string since the original input is then 0w1w and if they are not same then accept the input.

Hence by creating deterministic TM using above steps we will be able to recognize L.

Please comment for any clarification.