Question

What is the importance of the Turing Machine study on Computer Science?

What are the stopping conditions of a Turing Machine? Explain each one.

Answer 1

A Turing machine is a system of rules, states and transitions for deciding formal languages and solving mathematical functions.

1-Turing machine helps to propagate idea of algorithm in other practical machines. After the successful check of 1,2 criteria we can use our practical devices/computers to design and implement algorithm.

2-Designing of programming language (or anything else that is meant to compute things), then to ensure that it is Turing-complete (ie. capable of computing anything that is computable) by implementing a Turing machine in it.

3-Turing machine help define the 'class of problems' that are solvable/decidable by any computing device in a very precise manner and that helps really define 'computability' itself.

Stopping conditions of a Turing Machine:

1-A Turing machine can either eventually enter an accepting state, enter a rejecting state, or loop forever. If it enters either an accepting or rejecting state, then it halts.
2-When you can write a program for a Turing machine, whose input is another program for a Turing machine and some string of input, which returns true or false (halt-accepts or halt-rejects) if the program it has been given halts on the input provided and returns false otherwise