Algorithm (nonfiction)

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

Process

Starting from an initial state (nonfiction) and initial input (nonfiction) (perhaps empty (nonfiction)), the instructions (nonfiction) describe a computation (nonfiction) that, when 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 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 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

• Algorithm design (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)
• Maze generation algorithm (nonfiction)
• Mental model (nonfiction)
• Round-off error (nonfiction)
• Signal processing (nonfiction)

Fiction cross-reference

• Gnomon Algorithm

External links

• Algorithm @ Wikipedia