The Kleene star and Kleene plus operators used to express repetition in formal languages are idempotent.

In some formal language studies, ( e. g. AFL Theory ) a variation on the Kleene star operation called the Kleene plus is used.

In other words, the Kleene plus on is

The most common quantifiers are the question mark, the asterisk ( derived from the Kleene star ), and the plus sign ( Kleene cross ).

An example of an EXPSPACE-complete problem is the problem of recognizing whether two regular expressions represent different languages, where the expressions are limited to four operators: union, concatenation, the Kleene star ( zero or more copies of an expression ), and squaring ( two copies of an expression ).

Then the union ( written as +) and the concatenation ( written as ·) of two elements of A again belong to A, and so does the Kleene star operation applied to any element of A.

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, and Alan Turing's Turing machines of 1936 – 7 and 1939.

It is also a special case of De Morgan algebra and Kleene algebra.

# is a finite relation from to, where the asterisk represents the Kleene star operation.

* Church, along with mathematician Stephen Kleene and logician J. B. Rosser created a formal definition of a class of functions whose values could be calculated by recursion.

In the course of studying the problem, Church and his student Stephen Kleene introduced the notion of λ-definable functions, and they were able to prove that several large classes of functions frequently encountered in number theory were λ-definable.

Eventually, he would suggest his ( primitive ) recursion, modified by Herbrand's suggestion, that Gödel had detailed in his 1934 lectures in Princeton NJ ( Kleene and another student J.

Equipped with the λ-calculus and " general " recursion, Stephen Kleene with help of Church and J.

In a few years ( 1939 ) Turing would propose, like Church and Kleene before him, that his formal definition of mechanical computing agent was the correct one.

Kleene proposes Church's Thesis: This left the overt expression of a " thesis " to Kleene.

He relied heavily on earlier work by Stephen Kleene.

Papers include those by Godel, Church, Rosser, Kleene, and Post.

In mathematical logic and computer science, the Kleene star ( or Kleene operator or Kleene closure ) is a unary operation, either on sets of strings or on sets of symbols or characters.

Here the left-hand side represents the true difference between the value of g at a and at, whereas the right-hand side represents the approximation determined by the derivative plus an error term.

A term is an addend or a summand, a group of coefficients, variables, constants and exponents that may be separated from the other terms by the plus and minus operators.

; Lambda calculus: A computation consists of an initial lambda expression ( or two if you want to separate the function and its input ) plus a finite sequence of lambda terms, each deduced from the preceding term by one application of Beta reduction.

The academic year follows a 4 – 1 – 4 schedule of two four-course semesters plus a one-course " winter study " term in January.

The term Set-Back Box is used in the digital TV industry to describe a piece of consumer hardware that enables them to access both linear broadcast and internet-based video content, plus a range of interactive services like Electronic Programme Guides ( EPG ), Pay Per View ( PPV ) and Video on Demand ( VOD ) as well as internet browsing, and view them on a large screen television set.

For works authored by individuals on or after January 1, 1978 ( including new works ), the copyright term was extended to equal the life of the author plus 70 years.

For works authored by joint authors, the copyright term was extended to the life of the last surviving author plus 70 years.

A key factor in the CTEA ’ s passage was a 1993 European Union ( EU ) directive instructing EU members to establish a baseline copyright term of life plus 70 years and to deny this longer term to the works of any non-EU country whose laws did not secure the same extended term.

The output waveform contains the original waveform, cos ( ωt ), plus a new harmonic term, cos ( 3ωt ), the third-order.

Even further back, in 1978 Peter and Trudy Johnson-Lenz coined the term groupware ; their initial 1978 definition of groupware was, “ intentional group processes plus software to support them .” Later in their article they went on to explain groupware as “ computer-mediated culture ... an embodiment of social organization in hyperspace.

Factors of production are defined by Karl Marx in Das Kapital as labour, subjects of labour, and instruments of labour ; i. e., the term is equivalent to means of production plus labour.

Inner Mongolia is distinct from Outer Mongolia, which was a term used by the Republic of China and previous governments to refer to what is now the independent state of Mongolia plus the Republic of Tuva in Russia.

It can be seen that the velocity of a point in a rigid body can be divided into two terms – the velocity of a reference point fixed in the rigid body plus the cross product term involving the angular velocity of the particle with respect to the reference point.

This differs from the standard U. S. copyright term, life of the author plus 70 years, because the " author " of a work for hire is often not an actual person, in which case the standard term would be unlimited, which is unconstitutional.

The lower house is the Chamber of Deputies ( Cámara de Diputados ) with 178 members, elected for a four year term by proportional representation in accordance to each province, as follows: one deputy is elected for every 50, 000 inhabitants plus fraction exceeding 25, 000, but never less than two.

In reality, only the first term exists in modern Castilian, as it seems that the Spanish borrowed the Occitan name for themselves, which was the name España plus the diminutive suffix-ol, from the Latin-ulus or-olus.

Historically, the term Lothian is used for a province encompassing the present area plus the Scottish Borders region.

In the final chapter of his Evolution the modern synthesis he defines evolutionary progress as " a raising of the upper level of biological efficiency, this being defined as increased control over and independence of the environment ," Evolution in action discusses evolutionary progress at length: " Natural selection plus time produces biological improvement ... ' Improvement ' is not yet a recognised technical term in biology ... however, living things are improved during evolution ... Darwin was not afraid to use the word for the results of natural selection in general ...

It took the form to new heights using the London Festival Orchestra, a loose affiliation of Decca's classical musicians given a fictitious name adding the term " London " to sound impressive, to provide an orchestral linking framework to the Moodies already written and performed songs, plus overture & conclusion sections on the album including backing up Graeme Edge's opening & closing poems recited by Pinder.

For the term commencing on January 3, 2011, the Clark County Board of Commissioners set a schedule of salaries for constables in that county ranging from $ 1000 to $ 2050 per year plus statutory fees per NRS 258. 125 except for the Las Vegas Township Constable whose salary is fixed at $ 103, 456 per year.

Like copyright law in many other countries, Canada has a " life plus 50 " copyright term.

The Eastern Orthodox books included in the Old Testament are the seven deuterocanonical books listed above, plus 3 Maccabees and 1 Esdras ( also included in the Clementine Vulgate ), while Baruch is divided from the Epistle of Jeremiah, making a total of 49 Old Testament books in contrast with the Protestant 39-book canon.

Professional models have three top-action valves, played with the first three fingers of the right hand, plus a " compensating " fourth valve, generally found midway down the right side of the instrument, played with the left index finger ; such an instrument is shown in the above picture.

Most consist of a regular guitar, plus additional " harp " strings strung above the six normal strings.

* Windows 95 C-( OSR2. 5 ) included all the above features, plus IE 4. 0.

Many devices now sold as Hall effect sensors in fact contain both the sensor as described above plus a high gain integrated circuit ( IC ) amplifier in a single package.

In the eighties, many fighters defected to the rival World Karate Association ( WKA ) because of the PKA's policy of signing fighters to exclusive contracts ; plus, the PKA sanctioned fights exclusively with what has become known as " full contact rules " which permit kicks only above the waist as opposed to the international rules advocated by the WKA which is similar to kickboxing promotions in Japan and other countries in Asia and Europe.

The highest point in Lincoln is either the summit of Mount Carrigain, at above sea level, plus or minus, or the summit of Mount Bond at.

In Omaha, with the same board as above, a player holding 7 ♠ 8 ♠ plus 2-3 of any suit has the nut-nut and is guaranteed no worse than a split of the low pot plus a win of the high pot.

93 m in length and with a dome rising 35 m above the pavement at the north ( Stresemannstraße ) end, it contained the world ’ s largest restaurant-the 2, 500-seat Café Piccadilly, plus a 1, 200-seat theatre and numerous offices.

* Roger Wilco Unclogged ( 1995 ) – All the above, plus a humorous " Inside Space Quest " video, but without the Two Guys video

Company Grade ( O-3 or below ) commanders may impose the above plus:

Pioneer pastoralists, often men with experience as squatters in Australia, leased lands from the government at the annual rate of £ 5 plus £ 1 for each 1, 000 sheep above the first 5, 000.

The three-party ( i. e. six plus some purely Flemish and Walloon parties ) political systems got disturbed by the Green parties ( the Dutch-speaking Agalev, now Groen !, and the French-speaking Ecolo ) in the 1980s which took a lot of influence after the Marc Dutroux Scandal and the " dioxin affair ", a food scandal ( chickens containing dioxin levels far above the maximum allowed ) which would not have had any major repercussions, had it not erupted just days before the elections.

# Inner Manchuria: the above, plus parts of modern Inner Mongolia ( Hulunbuir, Hinggan, Tongliao, and Chifeng divisions );

# The above, plus Outer Manchuria ( Russian Manchuria ): the area from the Amur and Ussuri rivers to the Stanovoy Mountains and the Sea of Japan.

# The above, plus Sakhalin Island, which is generally included on Chinese maps as part of Outer Manchuria, even though it is not explicitly mentioned in the Treaty of Nerchinsk.

diameter of the Earth plus height of the observer above sea level

In 1963, he had an idea for expanding the Long Island Expressway capacity in Queens by adding three more lanes in each direction plus a second, four-lane deck above it.

: As above, plus presence of endometriomas on the ovary and more adhesions.

: As above, plus large endometriomas, extensive adhesions.

New stock would be created at a face value equal to the debt, but the share price was still rising and sales of the spare stock over and above that with a sale value equal to the debt would be used to raise the government fee plus a profit for the company.

) It is not generally recognized by the public that the increase in potential energy required to pass the Kármán line is only about 3 % of the orbital energy ( potential plus kinetic energy ) required by the lowest possible earth orbit ( a circular orbit just above the Kármán line.

Alternatively, the new economic order will incorporate all of the above plus other attributes that have not yet fully emerged.