Give an implementationlevel description of a Turing machine

Give an implementation-level description of a Turing machine that decides the following language L over the alphabet {a, b, c}. L = {w epsilon {a, b, c}*the number of a\'s minus the number of b\'s in w is at least zero, and equal to the number of c\'s in w} For examples of implementation-level descriptions of Turing machines, see examples 3.11 and 3.12 in your textbook.

Solution

1. Scan the string starting from left till the symbol \'a\' is found. Place a mark at that position.

2. Scan for symbol other than \'a\'. If found strike the symbol and go to marked position. Now strike marked position and scan for another \'a\'.

3. If no differnt symbol is found other than \'a\' then reject the given string.

4. If no \'a\' is found then reject the string.

5. After repeating steps 1 and 2 if string becomes empty then accept the string.