computational complexity theory In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved ...

, a computational resource is a resource used by some

computational model A computational model uses computer programs to simulate and study complex systems using an algorithmic or mechanistic approach and is widely used in a diverse range of fields spanning from physics, chemistry and biology to economics, psychology, ...

s in the solution of

computational problem In theoretical computer science, a computational problem is a problem that may be solved by an algorithm. For example, the problem of factoring :"Given a positive integer ''n'', find a nontrivial prime factor of ''n''." is a computational probl ...

s. The simplest computational resources are

computation time In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by t ...

, the number of steps necessary to solve a problem, and memory space, the amount of storage needed while solving the problem, but many more complicated resources have been defined. A computational problem is generally defined in terms of its action on any valid input. Examples of problems might be "given an integer ''n'', determine whether ''n'' is prime", or "given two numbers ''x'' and ''y'', calculate the product ''x''*''y''". As the inputs get bigger, the amount of computational resources needed to solve a problem will increase. Thus, the resources needed to solve a problem are described in terms of

asymptotic analysis In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that we are interested in the properties of a function as becomes very large. If , then as bec ...

, by identifying the resources as a function of the length or size of the input. Resource usage is often partially quantified using

Big O notation Big ''O'' notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by Paul Bachmann, Edmund L ...

. Computational resources are useful because we can study which problems can be computed in a certain amount of each computational resource. In this way, we can determine whether

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

s for solving the problem are optimal and we can make statements about an algorithm's efficiency. The set of all of the computational problems that can be solved using a certain amount of a certain computational resource is a

complexity class In computational complexity theory, a complexity class is a set of computational problems of related resource-based complexity. The two most commonly analyzed resources are time and memory. In general, a complexity class is defined in terms o ...

, and relationships between different complexity classes are one of the most important topics in complexity theory.

Describing generally accessible computing equipment

The term "Computational resource" is commonly used to describe accessible computing equipment and software. See

Utility computing Utility computing or The Computer Utility is a service provisioning model in which a service provider makes computing resources and infrastructure management available to the customer as needed, and charges them for specific usage rather than a ...

Formal quantification of computing capability

There has been some effort to formally quantify computing capability. A bounded

Turing machine A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer alg ...

has been used to model specific computations using the number of state transitions and alphabet size to quantify the computational effort required to solve a particular problem.

References

{{reflist, 1 Computational complexity theory