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Please draw the Turing machine with JFLAP format in paper by the following instruction.

To construct a linear bounded automaton (LBA) that accepts the language L = {a^n : n = m^2, m ? 1}, we need to make sure that the LBA accepts all strings that are in the language L and rejects all strings that are not in the language L.

One way to construct such an LBA is as follows:

1. The LBA reads the input string from the input tape and moves the head to the right end of the tape.

2. The LBA then marks the first symbol of the input string with a special symbol, say B.

3. The LBA then repeatedly checks if the string can be divided into two equal parts such that the first part consists of a^m symbols and the second part consists of a^n-m symbols, where n = m^2.

4. If the string cannot be divided into two such parts, then the LBA rejects the input string and halts.

5. If the string can be divided into two such parts, the LBA continues to repeat step 3 for each part.

6. For each part, the LBA marks the first symbol with a special symbol, say C.

7. The LBA then moves the head to the right end of the string and starts scanning the string from right to left.

8. For each a symbol encountered, the LBA moves one step to the left and changes the marked symbol from C to D.

9. The LBA continues this process until it has scanned all the symbols of the string.

10. If the LBA has marked all the symbols with D, then it accepts the input string. Otherwise, it rejects the input string.

The idea behind this LBA is to check if the input string can be divided into two parts such that the first part consists of a^m symbols and the second part consists of a^n-m symbols, where n = m^2.

If the string can be divided into such parts, then the LBA checks that each part contains a square number of a symbols. To do this, the LBA marks the first symbol of each part with the symbol C and scans the part from right to left,

marking each symbol with the symbol D as it goes. If the LBA can mark all the symbols with D, then the part contains a square number of a symbols. If the LBA can mark both parts with D,

then the entire string contains a square number of a symbols and the LBA accepts it.

To construct a linear bounded automaton that accepts L = {a^n : n = m^2, m ? 1}, we need to check if the string can be divided into two parts such that each part contains a square number of a symbols.

This can be done by marking the first symbol of each part with the symbol C and scanning the part from right to left, marking each symbol with the symbol D as it goes. If both parts can be marked with D,

then the entire string contains a square number of a symbols and the LBA accepts it.

I am not capable of drawing diagrams or graphics. However, I can provide you with a description of the Turing machine that you can create using JFLAP