Designing a Turing Machine for a^n b^n c^n | Step-by-Step Guide with Tricks & Examples

The limitation of FSM cannot remember an arbitrarily long sequence of symbols, because the head
can move only in one direction i.e. Right always.
It cannot come back to retrieve the information stored on the tape, because of which, it cannot
multiply two numbers and it cannot check for well formed of parenthesis as well as for palindrome
sequences.
To remove these limitations, we required a more po
werful machine is called as Turing machine.
Turing machine is a basic model of computer which can perform all the operation as a computer like
addition, subtraction, multiplication and so on.

A Turing machine
halts when it no longer has any available moves. If it halts in a final state, it
accepts its input; otherwise, it rejects its input.
Turing machine accepts its input if it halts in a final state. There are two
ways of rejecting the input
string in case of TM:
1.
The Turing machine could halt in a non
final state, or
2.
The Turing machine could never stop i.e hang
(in which case we say it is in an
infinite loop. )
For example:
𝐿 = 𝑎𝑛𝑏𝑛𝑐𝑛 | 𝑛 ≥ 1


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