Design a TM that perform right shift over ∑ = {0, 1}

Problem

Shift the input string right by one place and design a Turing Machine (TM) that can perform right shift over ∑ = {0, 1}.

Solution

Refer an algorithm given below to design a TM −

• Step 1 − Move right side to the last character from the initial character.

• Step 2 − If the character is „0?, replace it with „B? and move one step right to replace the immediate „B? to „0?.

• Step 3 − If the character is „1?, replace it with „B? and move one step right to replace the immediate „B? to „1?.

• Step 4 − After processing as above, move left one step to perform step 2 or 3 on the next right most unprocessed character.

• Step 5 − Perform step 4 until all the characters are processed.

The diagram given below shows the respective TM −

Description of Turing Machine

The Turing machine is given by M = (Q, Σ, Γ, δ, q0, B, F)

Where,

• Q = {q0, q1, q2, q3, q4, q5}

• Σ = {0, 1}

• Γ = {0, 1, B}

• q0 = {q0}

• B = {B}

• F = {q5}

Here,

• q0 → skips the initial 0?s and 1?s and moves the head of the TM to the last character. q1 → the unprocessed rightmost character is replaced by B.

• q2 → on processing the input „0?, q2 immediately replaces the „B? as „0? and takes left.

• q3 → on processing „1?, q3 replaces immediately the „B? as „1? and moves left.

• q4 → takes a left position to process the next character

  q5 → halts if no more input characters are available.