Difference between revisions of "Computational resource"
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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, 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]]. | 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, 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]]. | ||
| − | 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 for solving the problem are optimal and we can make statements about an algorithm's efficiency. | + | 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|algorithms]] for solving the problem are optimal and we can make statements about an [[Algorithmic efficiency|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]], and relationships between different complexity classes are one of the most important topics in [[complexity theory]]. | 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]], and relationships between different complexity classes are one of the most important topics in [[complexity theory]]. | ||
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== See also == | == See also == | ||
| + | * [[Algorithm]] | ||
| + | * [[Algorithmic efficiency]] | ||
| + | * [[Complexity class]] | ||
* [[Complexity theory]] | * [[Complexity theory]] | ||
* [[Computational complexity theory]] | * [[Computational complexity theory]] | ||
Latest revision as of 11:22, 20 September 2016
In computational complexity theory, a computational resource is a resource used by some computational models in the solution of computational problems.
The simplest computational resources are 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.
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, 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.
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 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, and relationships between different complexity classes are one of the most important topics in complexity theory.
See also
- Algorithm
- Algorithmic efficiency
- Complexity class
- Complexity theory
- Computational complexity theory
- Computational model
- Computational problem
External links
- Computational resource @ Wikipedia
