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# Design Turing Machine to reverse string consisting of a’s and b’s

Our aim is to design a Turing machine (TM) to reverse a string consisting of a’s and b’s over an alphabet {a,b}.

## Example

**Input** − aabbab

**Output** − babbaa

## Algorithm

Step 1: Move to the last symbol, replace x for a or x for b and move right to convert the corresponding B to „aâ€Ÿ or „bâ€Ÿ accordingly. Step 2: Move left until the symbol left to x is reached. Step 3: Perform step 1 and step 2 until „Bâ€Ÿ is reached while traversing left. Step 4: Replace every x to B to make the cells empty since the reverse of the string is performed by the previous steps.

The transition diagram for Turing Machine (TM) is as follows −

**Let us consider an example to check whether the given input is getting reverse or not **−

**Input string -** abb.

**Expected output -** {bba}

Therefore, the TM is as follows −

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