What is the use of studying theory of computation?

Answer 1

There are several uses. I will mention two.

One is to make calculations more efficient. For example, suppose you want to calculate x^2 + 2x + 4. Each operation is binary, that is, two inputs are converted to one output.

Option I

1. calculate x*x
2. calculate 2*x
3. add them together = x*x + 2*x
4. add 4 to the above.

or

Option II

1. calculate x+2
2. multiply by the above by x = x^2 + 2x
3. add 4 to the above.

That saves 1 binary operation in the calculation. If such a calculation is carried out thousands - or millions - of times, this small difference can save a lot of time.

Second, it is important to understand the behaviour of computation errors. Most rational numbers and all irrationals have infinitely long decimal - or binary - representations. Computers cannot work with infinitely long strings of digits and so need to truncate the numbers. This leads to rounding errors and understanding these is crucial in understanding the accuracy and limitations of your calculations.