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	Kleene star - Wikipedia, the free encyclopedia
		In mathematical logic and computer science, the Kleene star (or Kleene closure) is a unary operation, either on sets of strings or on sets of symbols or characters.
		It is widely used for regular expressions, which is the context in which it was introduced by Stephen Kleene to characterise certain automata.
		This is a generalization of the Kleene star discussed above since the set of all strings over some set of symbols forms a monoid (with string concatenation as binary operation).
	en.wikipedia.org /wiki/Kleene_closure (358 words)

	Kleene star
		The Kleene star is an operation used in regular expressions and operates either on sets of strings or on sets of symbols or characters.
		The Kleene star is named after Stephen Kleene (1909-1994) who introduced it when describing certain automata (see regular expression).
		The text of this article is licensed under the GFDL.
	www.ebroadcast.com.au /lookup/encyclopedia/kl/Kleene_closure.html (334 words)

	Stephen Kleene (Site not responding. Last check: 2007-10-08)
		Kleene was best known for founding the branch of mathematical logic known as recursion theory and for inventing regular expressions.
		The Kleene star and Ascending Kleene Chain are named after him.
		His son, Ken Kleene , wrote: "As far as I am aware this pronunciation is incorrect in all known languages.
	burks.brighton.ac.uk /burks/foldoc/86/111.htm (343 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		The set {01, 10} (00+11)* is the Kleene closure of the union of 0 concatenated with 0 and 1 concatenated with 1.
		The Kleene closure (star) is defined as the concatenation of none, one, two, or any countable number strings it applies to.
		Examples of Kleene star: 1* is the set of strings {epsilon, 1, 11, 111, 1111, 11111, etc. } This set is infinite.
	www.cumulativeinquiry.com /Problems/sqdefs.txt (1264 words)

	PlanetMath: Kleene star (Site not responding. Last check: 2007-10-08)
		The definition of Kleene star can be generalized so that it operates on any monoid
		See Also: alphabet, string, regular expression, Kleene algebra, language, convolution, weight (strings), weight enumerator
		This is version 2 of Kleene star, born on 2002-02-24, modified 2002-05-03.
	planetmath.org /encyclopedia/KleeneStar.html (155 words)

	AMCA: Some Results on Equational Axiomatization of Kleene Algebras by Igor Dolinka
		The other important role of Kleene algebras in theoretical computer science is that they serve as a part of dynamic algebras [], one of the main tools of modeling the work of computers in algebra and logic.
		Therefore, the equational theory of Kleene algebras is in an obvious correspondence with pairs of regular expressions (Kleene algebra terms) denoting the same regular language.
		In fact, it is known that the variety of Kleene algebras is also generated by the Kleene relation algebras, so that an equation holds in all Kleene relation algebras iff it holds in all Kleene algebras.
	at.yorku.ca /c/a/d/j/14.htm (1244 words)

	CMSC 451 Lecture 9, Intersection of languages, closure
		Regular languages are closed under operations: concatenation, union, intersection, complementation, difference, reversal, Kleene star, substitution, homomorphism and any finite combination of these operations.
		Concatenation, union and Kleene star are constructed using the corresponding regular expression to NFA technique.
		Sigma star is all possible strings over the alphabet sigma.
	www.csee.umbc.edu /~squire/cs451_l9.html (782 words)

	Common Text Transformation Library: Templatextl_opunarplus class Reference (Site not responding. Last check: 2007-10-08)
		Implements grammar evaluation method for Kleene star match algorithm, starting at the upper boundary of the parseable universe.
		Implements grammar evaluation method for Kleene star search algorithm, starting at the upper boundary of the parseable universe.
		Implements grammar evaluation method for Kleene star repeatable search algorithm, starting at the upper boundary of the parseable universe.
	cttl.sourceforge.net /classcttl__impl_1_1xtl__opunarplus.html (410 words)

	Middle East Open Encyclopedia: Asterisk (Site not responding. Last check: 2007-10-08)
		The asterisk is sometimes mistakenly referred to as an asterix, in a case of reverse etymology.
		In computer science, the asterisk is used in regular expressions to denote zero or more repetitions of a pattern; this use is known as the Kleene star or Kleene closure after Stephen Kleene.
		On a Touch-Tone telephone keypad, * (called star) is one of the two special keys, and is found on the left of the zero.
	www.baghdadmuseum.org /ref/?title=Asterisk (1343 words)

	CSC-223 97F : Outline of Class 33: Regular Expressions
		The Kleene star (repetation) of a regular expression, R is the union of epilon, R, RR, RRR, RRRR, and so on and so forth.
		Kleene star is notated by writing the RE with a subsequent star.
		Star has precedence over concatentation has precedence over alternation.
	www.math.grin.edu /~rebelsky/Courses/223/97F/Outlines/outline.33.html (959 words)

	Kleene Star Operator
		Has someone talked about integrating a Kleene star operator with first order logic.
		The Kleene star operator would operate as follow: (P1)*(P2) is interpreted as the predicate P1 occurring zero, one, or an infinite amount of times until predicate P2 is true.
		There has also been work done on a modal operator corresponding more closely to the Kleene star, in which P1 is a predicate true for a sequence of worlds, and P1* is true for a number of those sequences appended together ("choppy" logic).
	www.cs.kuleuven.ac.be /~dtai/projects/ALP/newsletter/archive_93_96/net/data-structs/kleene.html (579 words)

	Chapter 9 Regular Languages
		The set of regular languages is closed under union, concatenation, and the Kleene star.
		It is easy to form a regular expression that corresponds to the union of the two languages by putting a + between the two regular expressions.
		These operations form regular expressions that correspond to the concatenation and the Kleene star of the languages.
	www.mathsci.appstate.edu /~dap/classes/2490/chap9.html (764 words)

	[No title]
		(defun kleenep (rule) (and (rest rule) (listp (second rule)) (not (cdadr rule)))) ; This implements the extended Kleene star by checking for zero or more ; occurances of "item" separated by "separator"; "rule" holds the rest ; of the rule so we can match it when we can't match any more items and ; separators.
		I need this to get rid of a placeholder that "kleene" uses (to ; distinguish between an empty match and a failed match), so that ; "associate" doesn't get confused.
		This has the side effect of preventing ; the Kleene-star construct from matching the empty string when the ; delimiter is a nonterminal, which turns out to be very disirable behavior.
	www.cs.caltech.edu /~frechet/cs20/b/lab6/parse.lsp (1117 words)

	Regular Expressions (Site not responding. Last check: 2007-10-08)
		The asterisk used in regular expressions, the Kleene star, is named after him.
		Using the Kleene star operator, you can repeat sections of your regular expression to form an infinite set of strings.
		The starred portion is repeated any number of times, including none.
	home.earthlink.net /~mcdemarco/QA/regexp.html (683 words)

	[No title]
		STAR: curlp = lp; while (lp++ && lp[-1] != '\n'); goto star;* case WORD
		STAR: curlp = lp; while (lp++ && !isalnum(lp[-1])); goto star;* case CCHR
		STAR: curlp = lp; while (lp++ && trt[lp[-1]] == trt[ep]); ep++; goto star; case CCL
	www.rpi.edu /AFS/home/41/bailem2/rt/campus/usenet/trn/3.6/sgi_52/src/search.c (643 words)

	Fabulous Adventures In Coding : Regular Expressions From Scratch, Part Four: The Kleene Closure of a Language
		Definition 7: The union of two sets L and K is the set with all the members found in either, and is written L ∪ K. We're going to take the Kleene Star one level further and say that it applies to languages too.
		L* is the language consisting of set of strings, where those strings are any number of strings in L concatenated together.
		You probably noticed that the Kleene Star above only applied to the thing immediately to the star's left, whether the language or the symbol.
	blogs.msdn.com /ericlippert/archive/2005/11/28/496289.aspx (584 words)

	Kleene All-Star's 2001 Schedule
		2:45 PM 21 - Kleene All-Star's (Coed Team) vs.
		7:45 PM 30 - Kleen All-Star's (Coed Team) vs.
		9:00 PM 11 - Kleene All-Star's (Open Team) vs.
	www.cs.dartmouth.edu /~dwagn/kleene/schedule.html (44 words)

	Quick Start (Site not responding. Last check: 2007-10-08)
		Any expression that evaluates to a parser may be used with the Kleene Star.
		The Kleene Star is also known as a Kleene Closure, but we call it the Star in most places.
		In this case, the Kleene Star is modifying a more complex parser, namely, the one generated by the expression:
	www.boost.org /libs/spirit/doc/quick_start.html (1415 words)

	Re: Wish List: Prefix List for Token Definitions
		This grammar has characters and parentheses, as well as concatenation, multiplication and kleen operators.
		Why, because the parser has difficulty deciding whether the shift or reduce when it sees a "star" in an input that looks like: INPUT: abcd*...
		POSSIBILITIES (for "..."): (1) abcdabcd => reduce "abcd", because "" is a multiplication (2) abcd[EOF] => shift "", because "" is a kleene* operator.
	www.sable.mcgill.ca /listarchives/sablecc-list/msg00285.html (355 words)

	[No title]
		Theorem (Kleene's Theorem): L=L(M) for some DFA M (L = L(R) for some regular expression R. Sipser states this theorem slightly differently: Theorem (Sipser): A language is regular if and only if some regular expression describes it.
		4) R = R1(R2 5) R = R1(R2 6) R = R1* For the last three cases of the recursive definition we use the same constructions given in the proof that the class of regular languages is closed under union, concatenation, and Kleene star.
		This completes the proof of Lemma 1.29, which is the backward direction of Kleene's Theorem.
	www.utdallas.edu /~cshields/teach/automata_fall99/notes/auto_regexp_student.doc (2011 words)

	Regular expressions over characters
		This comprises the following operations: parentheses for marking embedded expressions, concatenation, disjunction, lists of alternative characters, unspecified character, optionality, Kleene star, and Kleene plus.
		Certain types of regular expressions can be abbreviated by the use of a 'flag'.
		It is a bit hard to think of natural language examples which match a regular expression where the Kleene operator takes a string of length 2 or longer as its argument.
	www.ims.uni-stuttgart.de /projekte/CorpusWorkbench/CQPUserManual/HTML/node13.html (605 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		operations on languages: concatenation of strings, union, intersection, Kleene star
		Here we are going to learn the concept of language in very abstract and general sense, operations on languages and some of their properties.
		is also the same Kleene star defined above.
	www.cs.odu.edu /~toida/nerzic/390teched/language/definitions.html (588 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Though it is significantly easier, keep in mind that you limit the number of states you can use, which is a problem if you are inefficient with your states.
		As Professor H.T. Kung is so fond of saying, “Life is Hard.” The Kleene star is named after Stephen Kleene.
		The Kleene Plus is named after his fish, Eric Kleene.
	www.eecs.harvard.edu /~vernal/learn/cs51/Section-09.doc (1301 words)

	Basic Concepts (Site not responding. Last check: 2007-10-08)
		Like the binary composite, the unary composite may change the behavior of its embedded subject.
		The Kleene star, when called, calls its sole subject zero or more times.
		"Zero or more" implies that the Kleene star always returns a successful match, possibly matching the null string: "".
	spirit.sourceforge.net /dl_docs/spirit_v1_5/doc/basic_concepts.html (1202 words)

	CSCI 405, Fall 2004, Assignment 1
		Patterns may include pattern-variables (symbols that have been defined by some means to be variables) and Kleene star represented by the symbol "*".
		p is NOT ;ADVANCED, but d is. That is, in the recursive call ;p will still have kleene star as its head ;but d will be its cdr.
		starts with a symbol that is not a variable, nor a a Kleene Star.
	cs.uwp.edu /Classes/Cis605/Assignments/a1.html (1094 words)

	CorpusQueryProcessor - Lab Software and Corpora
		The Kleene star (which means "one or more") when you want to indicate repetition.
		The Kleene star and plus are often used with the wildcard character (.) which can stand for any character.
		Here is an example of how the Kleene star (*) is used:
	bulba.sdsu.edu /docwiki/CorpusQueryProcessor (2126 words)

	Information and Computation Bibliography (Site not responding. Last check: 2007-10-08)
		Multi-exit iteration is a generalization of the standard binary Kleene star operation that allows for the specification of agents that, up to bisimulation equivalence, are solutions of systems of recursion equations of the form
		As a consequence, the proof of completeness of the proposed equational axiomatization for this language, although standard in its general structure, is much more involved than that for BPA*.
		A completeness theorem for Kleene algebras and the algebra of regular events.
	theory.lcs.mit.edu /~iandc/References/acetof1997:121.html (262 words)

	Kleene Star Closure of Finite State Automata (Site not responding. Last check: 2007-10-08)
		Given a finite state automaton M, this transformation constructs another FSA M' which recognises the kleene star of the language.
		We use the appropriate algorithm to obtain a regular grammar which recognises the Kleene star closure of the language recognised by the above grammar:
		Construct FSA which recognise the Kleene star closure of the following languages described using FSA:
	www.cs.chalmers.se /~gpace/Research/Software/Relic/Transformations/FSA/kleene-star.html (119 words)

	Operator Precedence
		According to this table, the high-precedence crossproduct operator : outranks everything else, followed by the prefix operators such as ~ (complement) \ (term complement), and $ (contains) that are said to outrank suffix operators such as * (Kleene plus) and + (Kleene star) and other iteration operators.
		This is true only for the term complement operator \ but false for the other prefix operators, as illustrated by the examples below:
		It includes the substitution operator ` (see page 51 in the book) that was inadvertently left out of the original table and the precede < and follow operators that appear in the precedence table but are not discussed anywhere in the book.
	www.stanford.edu /~laurik/fsmbook/errata/precedence.html (333 words)

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