Algorithm

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

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