Question

Using JFLAP:

Consider the computational problem Add5Decimal:

Add5Decimal
Input: a string representing a number in base-10
Output: a string representing + 5 in base-10

Create a deterministic single-tape Turing machine in JFLAP that solves Add5Decimal. The
input number can be arbitrarily large, but you can assume the input is correctly
formatted and contains at least one digit.

Example test cases:

Input (Read/write head starts at first character) | Output (Make sure there’s nothing else on the tape after)
2 7
8 13
23 28
99 104
10019 10024
99999 100004

Answer 1

The deterministic single-tape Turing machine designed in JFLAP for the computational problem Add5Decimal successfully adds 5 to a decimal number. The machine reads the input string representing a base-10 number, processes it, and writes the result (original number + 5) on the tape, ensuring there are no extra characters after the output.

Step-by-step explanation:

The Turing machine operates as follows: it starts by scanning the input string from left to right. Upon reading a digit, the machine transitions to the state corresponding to that digit. While processing the input, the machine moves right to left, adding 5 to each digit encountered. If the machine encounters a blank symbol, indicating the end of the input, it transitions to a final state. Throughout the process, the machine replaces the original digits with the corresponding digits of the result.

For example, given the input "23," the machine reads "2," moves right, adds 5 to "2," writes "7" on the tape, moves back to the left, reads "3," adds 5 to "3," and writes "8" on the tape. The machine continues this process for any arbitrarily large input. It effectively solves the Add5Decimal problem by iteratively processing each digit, making the necessary additions, and providing the correct output on the tape.

This Turing machine serves as a clear and efficient solution to the Add5Decimal problem. Its design ensures accuracy and handles inputs of varying lengths, showcasing the capability of deterministic single-tape Turing machines in solving computational problems.