Theory of Computation:

The theory of computation is the branch of computer science that deals with whether and how efficiently problems can be solved on a computer. The field is divided into two major branches: computability theory and complexity theory, but both branches deal with formal models of computation.

In order to perform a thorough study of computation, computer scientists work with a mathematical abstractions of computers called a model of computation. There are several formulations in use, but the most commonly examined is the Turing machine. A Turing machine can be thought of as a desktop PC with an infinite memory capacity, though it can only access this memory in small separate chunks. Computer scientists study the Turing machine because it is simple to formulate, can be analyzed and used to prove results, and because it represents what many consider the most powerful possible "reasonable" model of computation. While the infinite memory capacity might be considered an unphysical attribute, for any problem actually solved by a Turing machine the memory used will always be finite, so any problem that can be solved on a Turing machine could be solved on a desktop PC which has enough memory installed.