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In [[mathematics (nonfiction)]] and [[computer science (nonfiction)]], an '''algorithm''' is a self-contained step-by-step set of [[Operation (nonfiction)|operations (nonfiction)]] to be performed.
In [[mathematics (nonfiction)]] and [[computer science (nonfiction)]], an '''algorithm''' is a self-contained step-by-step set of operations to be performed.
 
== Description ==
 
Algorithms exist that perform [[calculation (nonfiction)]], [[data processing (nonfiction)]], and [[automated reasoning (nonfiction)]].
 
An algorithm is an effective method that can be expressed within a finite amount of [[space (nonfiction)]] and [[time (nonfiction)]] and in a well-defined [[formal language (nonfiction)]] for calculating a [[Mathematical function (nonfiction)|mathematical function (nonfiction)]].
 
== Process ==
 
Starting from an [[initial state (nonfiction)]] and [[initial input (nonfiction)]] (perhaps [[empty (nonfiction)]]), the [[Instruction (nonfiction)|instructions (nonfiction)]] describe a [[computation (nonfiction)]] that, when [[Execution (nonfiction)|executed (nonfiction)]], proceeds through a [[finite number (nonfiction)]] of [[well-defined successive states (nonfiction)]], eventually producing [[output (nonfiction)]] and [[terminating at a final ending state (nonfiction)]].
 
== Randomized algorithms ==
 
The transition from one [[state (nonfiction)]] to the next is not necessarily deterministic; some algorithms, known as [[Randomized algorithm (nonfiction)|randomized algorithms (nonfiction)]], incorporate [[random input (nonfiction)]].
 
== 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 (nonfiction)]]'' (the "decision problem") posed by [[David Hilbert (nonfiction)]] 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 (nonfiction)]]'s [[lambda calculus (nonfiction)]] of 1936
* Emil Post's "Formulation 1" of 1936
* [[Alan Turing (nonfiction)]]'s [[Turing machine (nonfiction)|Turing machines (nonfiction)]] 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 (nonfiction)]] is an important part of a broader [[computational complexity theory (nonfiction)]], which provides theoretical estimates for the resources needed by any algorithm which solves a given [[computational problem (nonfiction)]].
 
These estimates provide an insight into reasonable directions of search for [[algorithmic efficiency (nonfiction)]].


== Nonfiction cross-reference ==
== Nonfiction cross-reference ==


* [[Algorithm design (nonfiction)]]
* [[Computer science (nonfiction)]]
* [[Algorithmic efficiency (nonfiction)]]
* [[Analysis of algorithms (nonfiction)]]
* [[Automated reasoning (nonfiction)]]
* [[Automaton (nonfiction)]]
* [[Calculation (nonfiction)]]
* [[Combinatorics (nonfiction)]]
* [[Computational complexity theory (nonfiction)]]
* [[Computational problem (nonfiction)]]
* [[Data processing (nonfiction)]]
* [[Entscheidungsproblem (nonfiction)]]
* [[Function (mathematics) (nonfiction)]]
* [[Genetic algorithm (nonfiction)]]
* [[Gnomon Algorithm (nonfiction)]]
* [[Kruskal's algorithm (nonfiction)]]
* [[Mathematical model (nonfiction)]]
* [[Mathematics (nonfiction)]]
* [[Mathematics (nonfiction)]]
* [[Maze generation algorithm (nonfiction)]]
* [[Mental model (nonfiction)]]
* [[Round-off error (nonfiction)]]
* [[Signal processing (nonfiction)]]


== Fiction cross-reference ==
== Fiction cross-reference ==


* [[Gnomon Algorithm]]
* [[Gnomon Algorithm]]
* [[Mathematics]]


== External links ==  
== External links ==  

Revision as of 08:23, 27 May 2016

In mathematics (nonfiction) and computer science (nonfiction), an algorithm is a self-contained step-by-step set of operations to be performed.

Nonfiction cross-reference

Fiction cross-reference

External links

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