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In computer science and mathematics, computer theory is the branch that deals with how efficiently one can solve problems in a computer model, using an algorithm. The field is divided into three main branches: automata theory and language, computability theory and computational complexity theory, which are linked by the question: "What are the fundamental capabilities and limitations of computers?"
To perform a rigorous study of computing, computer scientists work with a mathematical abstraction of computers called a computer model. There are several models in use, but the most commonly examined is the Turing machine. Computer scientists study the Turing machine because it is simple to formulate, it can be analyzed and used to test the results, and because it represents what many consider the most "powerful" reasonable computing model possible (see the Church-Turing thesis). It might seem that potentially infinite memory capacity is an unrealisable attribute, but any problem that can be resolved solved by a Turing machine will always require only a finite amount of memory. So, in principle, any problem that can be solved (decided) by a Turing machine can be solved by a computer that has a finite amount of memory.
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