Considering both the theoretical computer science and mathematics, the theory of computation is a sector which is focused on how efficiently problems can be solved on a model of computation by adopting algorithm. The area is divided into three branches which are: the automata theory and languages, the computability theory and the computational complexity theory.
The automata theory is the study of abstract machines and automata. The theory is used both in theoretical computer science and discrete mathematics and focuses on computational problems. As well as this, it analyses how these issues can be solved by the adoption of abstract machines.
The computational theory is a branch of mathematical logic and computer science which deal with the difficulty of the problem. This theory outlines to which extent the problem is solvable by a computer.
Computational complexity theory is a branch of computation that focuses on classifying computational problems according to their difficulty. Additionally, it focuses on how efficiently the problem can be solved considering the time and space complexity.
As to develop a sophisticated study of computations, computer scientists work with mathematical abstractions of computers, known as models of computations. Currently, scientists adopt different models; however, the Turing machine is the most adopted one as it is easy to use and prove results.
The Turing machine was invented in 1936 by Alan Turing. This is a mathematical model of computation which defines an abstract machine and manipulates symbols which are set on a strip of tape according to a set of rule. The machine works on an infinite memory tape which is divided into cells and can read and write symbols on each cell.
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