# Computational resource

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For other uses, see [Resource (computer science) (disambiguation)](/source/Resource_(computer_science)_(disambiguation)).

In [computational complexity theory](/source/Computational_complexity_theory), a **computational resource** is a resource used by some [computational models](/source/Computational_model) in the solution of [computational problems](/source/Computational_problem).

The simplest computational resources are [computation time](/source/Computation_time), 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.[citation needed]

A computational problem is generally[citation needed] 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](/source/Asymptotic_analysis), 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](/source/Big_O_notation).

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 [algorithms](/source/Algorithm) for solving the problem are optimal and we can make statements about an [algorithm's efficiency](/source/Algorithmic_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](/source/Complexity_class), 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](/source/Utility_computing).

## Formal quantification of computing capability

There has been some effort to formally quantify computing capability. A bounded [Turing machine](/source/Turing_machine) 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.[1][2]

## See also

- [Compute (machine learning)](/source/Compute_(machine_learning))

## References

1. Gregory J., Chaitin (1966). ["On the Length of Programs for Computing Finite Binary Sequences"](https://web.archive.org/web/20070205042653/http://www.cs.auckland.ac.nz/CDMTCS/chaitin/acm66.pdf). *[Journal of the ACM](/source/Journal_of_the_ACM)*. **13** (4): 547–569. [doi:10.1145/321356.321363](https://doi.org/10.1145/321356.321363). [S2CID 207698337](https://api.semanticscholar.org/CorpusID:207698337). Archived from [the original](http://www.cs.auckland.ac.nz/CDMTCS/chaitin/acm66.pdf) on 2007-02-05. Retrieved 2007-09-25.

1. Sow, Daby & Eleftheriadis, Alexandros (1998). [*Representing Information with Computational Resource Bounds*](http://www.ee.columbia.edu/ln/dvmm/publications/98/daby_eleft_asilomar98.pdf). Signals, Systems & Computers. Conference Record of the Thirty-Second Asilomar Conference on. Vol. 1. pp. 452–456. ISBN 0-7803-5148-7. 10.1109/ACSSC.1998.750904. Retrieved 2007-09-25.

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Adapted from the Wikipedia article [Computational resource](https://en.wikipedia.org/wiki/Computational_resource) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Computational_resource?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.