Difference between revisions of "Algorithm"
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| − | In [[mathematics]] and [[computer science]], an '''algorithm''' (Listeni/ˈælɡərɪðəm/ al-gə-ri-dhəm) is a self-contained step-by-step set of operations to be performed. | + | In [[mathematics]] and [[computer science]], an '''algorithm''' (Listeni/ˈælɡərɪðəm/ al-gə-ri-dhəm) is a self-contained step-by-step set of [[operations]] to be performed. |
== Description == | == Description == | ||
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Algorithms exist that perform [[calculation]], [[data processing]], and [[automated reasoning]]. | Algorithms exist that perform [[calculation]], [[data processing]], and [[automated reasoning]]. | ||
| − | An algorithm is an effective method that can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. | + | An algorithm is an effective method that can be expressed within a finite amount of [[space]] and [[time]] and in a well-defined [[formal language]] for calculating a [[Function (mathematics)|function]]. |
== Process == | == Process == | ||
Revision as of 17:22, 1 September 2015
In mathematics and computer science, an algorithm (Listeni/ˈælɡərɪðəm/ al-gə-ri-dhəm) is a self-contained step-by-step set of operations to be performed.
Contents
Description
Algorithms exist that perform calculation, data processing, and automated reasoning.
An algorithm is an effective method that can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function.
Process
Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing output and terminating at a final ending state.
Randomized algorithms
The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.
History
The concept of algorithm has existed for centuries, however a partial formalization of what would become the modern algorithm began with attempts to solve the Entscheidungsproblem (the "decision problem") posed by David Hilbert in 1928.
Effective calculability
Subsequent formalizations were framed as attempts to define "effective calculability" or "effective method".
Those formalizations included:
- The Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935
- Alonzo Church's lambda calculus of 1936
- Emil Post's "Formulation 1" of 1936
- Alan Turing's Turing machines of 1936–7 and 1939.
Giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem.
Algorithm analysis
Analysis of algorithms is an important part of a broader computational complexity theory, which provides theoretical estimates for the resources needed by any algorithm which solves a given computational problem.
These estimates provide an insight into reasonable directions of search for algorithmic efficiency.
See also
- Algorithm design
- Algorithmic efficiency
- Analysis of algorithms
- Automated reasoning
- Calculation
- Combinatorics
- Computational complexity theory
- Computational problem
- Data processing
- Entscheidungsproblem
- Function (mathematics)
- Kruskal's algorithm
- Mathematical model
- Mathematics
- Maze generation algorithm
- Mental model
- Signal processing
External links
- Algorithm @ Wikipedia
