The set of equations ( 5 ), ( 6 ), and the starting equation ( 7 ) is of a recursive type well suited to programming on the digital computer.

Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.

In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive.

However, the recursion is bounded because in each recursive application either m decreases, or m remains the same and n decreases.

If we define the function f ( n ) = A ( n, n ), which increases both m and n at the same time, we have a function of one variable that dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi-and superfactorial functions, and even functions defined using Knuth's up-arrow notation ( except when the indexed up-arrow is used ).

This extreme growth can be exploited to show that f, which is obviously computable on a machine with infinite memory such as a Turing machine and so is a computable function, grows faster than any primitive recursive function and is therefore not primitive recursive.

Seed AI is a hypothesized type of strong artificial intelligence capable of recursive self-improvement.

A common adaptive method is recursive subdivision, in which a curve's control points are checked to see if the curve approximates a line segment to within a small tolerance.

The recursive equation is best introduced in a slightly more general form

Although the above recursive formula can be used for computation it is

It is not feasible to carry out such a computation using the above recursive formulae, since at least ( a constant multiple of ) p < sup > 2 </ sup > arithmetic operations would be required.

Note that this is different from the recursive languages which can be decided by an always-halting Turing machine.

Note that the set of grammars corresponding to recursive languages is not a member of this hierarchy.

Every regular language is context-free, every context-free language, not containing the empty string, is context-sensitive and every context-sensitive language is recursive and every recursive language is recursively enumerable.

* ATLAS is an acronym for Association for Tourism and Leisure Education, a European educational project

APL is an abbreviation, acronym, or initialism that may refer to:

* AOTUS is also the acronym for the Archivist of the United States

ACN is a three-letter acronym that may refer to:

The Asociación Latinoamericana de Integración ( the Latin American Integration Association ; known as ALADI or, occasionally, by the English acronym LAIA ) is a Latin American trade integration association, based in Montevideo.

The Old Testament is called by the Jews the Tanakh, an acronym formed by combining the initials of the three sections by which the Jews divide the text: the Torah, or Law ( the Pentateuch ), the Nevi ' im, or Prophets, and the Ketuvim, or Writings or Hagiographa ( with vowels added, as Hebrew is written with a consonantal script, TaNaKh ).

BASIC is a family of general-purpose, high-level programming languages whose design philosophy emphasizes ease of use ; the name is an acronym from Beginner's All-purpose Symbolic Instruction Code.

The acronym is tied to the name of an unpublished paper by Thomas Kurtz and is not a backronym.

" BASE " is an acronym that stands for four categories of fixed objects from which one can jump: buildings, antennas, spans ( bridges ), and earth ( cliffs ).

The name itself is an acronym, a pun, and a description.

Capitalised, BASIC is sometimes taken as an acronym that stands for British American Scientific International Commercial.

The global youth movement is known as NOAM ( an acronym for No ' ar Masorti ); its North American chapter is called the United Synagogue Youth.

Its name is an acronym for COmmon Business-Oriented Language, defining its primary domain in business, finance, and administrative systems for companies and governments.

The theory that the word originated as an acronym from the names of the group of ministers is a folk etymology, although the coincidence was noted at the time and could possibly have popularized its use.

PID is an acronym for Proportional-Integral-Derivative, referring to the three terms operating on the error signal to produce a control signal.

* CNS is a short acronym in musical jargon to reference the catalog numbering systems for single records

* ( Hanukkah ) is also the Hebrew acronym for — " Eight candles, and the halakha is like the House of Hillel ".

The acronym, ' DIN ,' is often incorrectly expanded as (" German Industry Standard ").

Digital Enhanced Cordless Telecommunications ( Digital European Cordless Telecommunications ), usually known by the acronym DECT, is a digital communication standard, which is primarily used for creating cordless phone systems.

* Nagios — Nagios Ain't Gonna Insist On Sainthood ( which is a reference to the previous name of Nagios, namely Netsaint )

Nagios () is an open source computer system monitor, network monitoring and infrastructure monitoring software application.

Nagios, originally created under the name NetSaint, was written and is currently maintained by Ethan Galstad, along with a group of developers actively maintaining both official and unofficial plugins.

Nagios is Open Source Software licensed under the GNU GPL V2.

Nagios Remote Plugin Executor ( NRPE ) is a Nagios agent that allows remote systems monitoring using scripts that are hosted on the remote systems.

Nagios Remote Data Processor ( NDRP ) is a Nagios agent with a flexible data transport mechanism and processor.

Nagios plugin that is used to collect information from this addon is called.

: Black women and feminism is a 1981 book by bell hooks titled after Sojourner Truth's " Ain't I a Woman?

On " Ain't it Funky " ( c. late 1960s ), and " Give it Up or Turn it Lose " ( 1969 ), the tonal structure is bare bones.

One of his most famous numbers is " They Ain't Makin ' Jews Like Jesus Anymore ," a song in which Kinky verbally and physically beats up a drunken white racist who berates blacks, Jews, Greeks, and Sigma Nus in a bar.

The name LAME is a recursive acronym for " LAME Ain't an MP3 Encoder ".

Gage's version of the speech became the historic standard, and is known as " Ain't I a Woman?

The album is also notable for containing a number of covers of songs by other artists, including The Ramones (" The Return of Jackie and Judy " and " Danny Says "), Daniel Johnston (" King Kong "), Kurt Weill and Bertolt Brecht (" What Keeps Mankind Alive "), and Leadbelly (" Ain't Goin ' Down to the Well " and " Goodnight Irene "), as well as renditions of works by poets and authors admired by Waits, such as Charles Bukowski and Jack Kerouac and a previously released duet with Mark Linkous of Sparklehorse entitled " Dog Door ".

* Ain't Nobody's Business If You Do ( ISBN 0-931580-58-7 ) is a book by Peter McWilliams criticizing the existence of laws against consensual crimes.

( The title is an acronym for There Ain't No Such Thing As A Free Lunch!

The book first publicized the acronym TANSTAAFL (" There Ain't No Such Thing As A Free Lunch "), and helped popularize the constructed language Loglan, which is used in the story for precise human-computer interaction.

Before each home game, a video package of team highlights and the pre game theme of " Ain't No Grave " by Johnny Cash is played.

Although in the end, the animator is revealed to be Daffy's rival Bugs Bunny ( who famously declares " Ain't I a stinker?

If all three major market indices are lower, " Stormy Weather " is the background music (" We're in the Money " is played if markets are up, and " It Don't Mean a Thing ( If It Ain't Got That Swing )" is played if markets are mixed ).

After unsuccessfully trying to plead his innocence ( by reciting the lyrics of Bob Dylan's " It Ain't Me Babe " and insisting that he did no more than " cross an imaginary line with a bunch of plants "), George skips bail to take care of Barbara, who is suffering from, and eventually succumbs to, cancer.

" Putting in a telephone call to that town's Chief of Police in advance, Thurber is told by a desk sergeant, " Ain't no violence over here.

For example, " TANSTAANFS " is used by electrical engineering professors to stand for " There Ain't No Such Thing As A Noise Free System ".

For example, Lenny Kravitz is listed for " It Ain't Over ' til It's Over " ( No. 2, August 1991 ); the book therefore misses subsequent hits, such as " Fly Away ", which peaked at # 12 in 1999, and " Again ", which peaked at # 4 in 2001, on the Hot 100.

An example is the remix of " Ain't It Funny " by Jennifer Lopez, which has little in common with the original recording apart from the title.

Ain't Misbehavin is a musical revue with a book by Murray Horwitz and Richard Maltby, Jr., and music by various composers and lyricists.

It is named after the song by Fats Waller ( with Harry Brooks and Andy Razaf ), " Ain't Misbehavin '".

The musical is a tribute to the black musicians of the 1920s and ' 30s who were part of the Harlem Renaissance, an era of growing creativity, cultural awareness, and ethnic pride, and takes its title from the 1929 Waller song " Ain't Misbehavin '".

On Snoop Dogg's Doggystyle album, Warren G and Daz Dillinger claim they produced " Ain't No Fun ", even though Dre is credited as the album's sole producer.

* When Roy is sitting in the hotel talking with the mayor's daughters, we hear " Ain't misbehavin " being played by the pianist in the background.