Theory of computation

According to Peter J. Denning, the fundamental question underlying computer science is, "What can be (efficiently) automated?"^[8] The study of the theory of computation is focused on answering fundamental questions about what can be computed and what amount of resources are required to perform those computations. In an effort to answer the first question, computability theory examines which computational problems are solvable on various theoretical models of computation. The second question is addressed by computational complexity theory, which studies the time and space costs associated with different approaches to solving a multitude of computational problems.

The famous "P=NP?" problem, one of the Millennium Prize Problems,^[21] is an open problem in the theory of computationThe broader field of theoretical computer science encompasses both the classical theory of computation and a wide range of other topics that focus on the more abstract, logical, and mathematical aspects of computing