Theory of computation is a branch of multiple fields, where the most important ones are computer science and mathematics. The initial approach was to mathematics, where by using algorithms, it measured the level of efficiency of a current problem. It can compute man-made problems as well as natural phenomena.
The main focus if Theory Computation is divided into three parts:
2. Computability theory 3. Computational Complexity theory
An automaton is a series of action that determines whether an action should be rejected or accepted. It is developed in states and each state has information about what to do when an input is received by the machine. As many times as the machine is given a new input, it goes back to the state and changes the spot naturalized by the kind of input and takes instruction how to deal with it. When there are no more inputs, the automaton stops and the space it is on when it completes determines whether the automaton declares that it accepts or rejects that particular set of inputs.
Computability theory and complexity are the ordering of problems in their level of difficulty and the actual approach if a problem can be computed, solved in computational manners.
Computation theory has a lot of applications in real life as well, such that: Lambda calculus, Combinatory logic, Markov algorithm, and Register machine.
Also, the theory of computation can overlap with other subjects as well. Two main cluster are complexity theory and algorithms. (Goldreich). As a result, theory of computation has shown a significant impact on the world of computer science.
Reference https://toc.seas.harvard.edu/ http://www.csc.villanova.edu/~japaridz/CL/ https://theory.org/complexity/cdpt/html/node3.html
Questions :
1- Can we reach a point where no problem is unsolvable for computers? 2- How can theory in computational theory be turned into practice more efficiently? 3- A lot of other subjects brought development to computer science through computational theory. What development does CS bring to other subjects ?