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Topic: Kleene closure

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Kleene star

Kleene algebra

Regular expression

Algebraic structure

Nondeterministic finite state machine

Stephen Cole Kleene

Automata theory

Deterministic finite state machine

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	Stephen Cole Kleene - Wikipedia, the free encyclopedia
		Kleene was best known for founding the branch of mathematical logic known as recursion theory together with Alonzo Church, Kurt Gödel, Alan Turing and others; and for inventing regular expressions.
		Kleene's standing in mathematical logic is reflected in the proverb "Kleeneliness is next to Gödeliness" among logicians (a pun on "Cleanliness is next to godliness").
		An avid mountain climber, Kleene had a strong interest in nature and the environment and was active in many conservation causes.
	en.wikipedia.org /wiki/Stephen_Kleene (458 words)

	Closure (Site not responding. Last check: 2007-10-11)
		In general, a closure is constructed by adding elements to a set until it stops growing.
		For ε closure, for example, "reachability" is defined in terms of ε transitions.
		Kleene closure for languages is also a closure computation.
	www.cs.buffalo.edu /~drpierce/cse/443/lectures/closure.html (503 words)

	Station Information - Kleene star
		The Kleene star (or Kleene closure) is an operation used in regular expressions and operates either on sets of strings or on sets of symbols or characters.
		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).
		The Kleene star is named after Stephen Kleene (1909-1994) who introduced it when describing certain automata (see regular expression).
	www.stationinformation.com /encyclopedia/k/kl/kleene_star.html (325 words)

	Closure (computer science) - Wikipedia, the free encyclopedia
		Closures are typically implemented with a special data structure that contains a pointer to the function code, plus a representation of the function's lexical environment (i.e., the set of available variables and their values) at the time when the function was created.
		Closures are closely related to Actors in the Actor model of concurrent computation where the values are called acquaintances.
		Closures typically appear in languages that allow functions to be first-class values—in other words, such languages allow functions to be passed as arguments, returned from function calls, bound to variable names, etc., just like simpler types such as strings and integers.
	steike.com /PhpClosures/2a18fd8f4a5b1362a34784adc2115c18 (735 words)

	Stephen Cole Kleene (Site not responding. Last check: 2007-10-11)
		Stephen Cole Kleene (January 5, 1909 - January 25, 1994) was an American mathematician whose work at the University of Wisconsin - Madison helped lay the foundations for theoretical computer science.
		By providing methods of determining which problems are solvable, Kleene's work led to the study of which functions are computable.
		He was an instructor of navigation at the U.S. Naval Reserve's Midshipmen's School in New York, and then a project director at the Naval Research Laboratory in Washington, D.C
	www.bidprobe.com /en/wikipedia/s/st/stephen_cole_kleene.html (408 words)

	Closure (computer science) -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-11)
		Closures are typically implemented with a special ((computer science) the organization of data (and its storage allocations in a computer)) data structure that contains a pointer to the function code, plus a representation of the function's lexical environment (i.e., the set of available variables and their values) at the time when the function was created.
		Closures typically appear in languages that allow functions to be (Click link for more info and facts about "first-class" values) "first-class" values—in other words, such languages allow functions to be passed as arguments, returned from function calls, bound to variable names, etc., just like simpler types such as strings and integers.
		To approximate an actual closure, one can imagine placing all global variables in a single struct, a copy of which can be passed to a function object.
	www.absoluteastronomy.com /encyclopedia/C/Cl/Closure_(computer_science).htm (719 words)

	Kleene algebra mathematics Stephen Cole Kleene distributive lattice Boolean algebra algebraic structure category binary ... (Site not responding. Last check: 2007-10-11)
		In fact, this is a "free" Kleene algebra in the sense that any equation among regular expressions follows from the Kleene algebra axioms and is therefore valid in every Kleene algebra.
		Kleene algebras were not defined by Kleene; he introduced regular expressions and asked for a set of axioms which would allow to derive all equations among regular expressions.
		The axioms of Kleene algebras solve this problem, as was first shown by Dexter Kozen.
	en.powerwissen.com /R7qo3W%2BpnhhOsaUzBKc%2Bdw%3D%3D_Kleene_algebra.html (1143 words)

	[No title] (Site not responding. Last check: 2007-10-11)
		The building blocks of regular languages are symbols, concatenation of symbols to make strings (words), set union of strings and Kleene closure (denoted as , also called the Kleene* star, it should be typed as a superscript but this is plain text.) Informally, we use a syntax for regular expressions.
		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.
	www.cumulativeinquiry.com /Problems/sqdefs.txt (1264 words)

	Finite-state automata and regular languages
		Kleene (1956)'s ``regular events''; in other words, if a language is accepted by a DFA, it is a regular language, and vice versa.
		) or more times (this operation is called the Kleene closure and the symbol is called the Kleene star); using these operations (concatenation, union, and Kleene closure) on regular languages always yields regular languages.
		Kleene (1956) showed for the first time that the set of languages expressible by regular expressions is exactly the one that may be accepted by a net with circles, that is, by a finite-state machine (see also
	www.dlsi.ua.es /~mlf/nnafmc/pbook/node17.html (253 words)

	Operations on transducers (Site not responding. Last check: 2007-10-11)
		Therefore, the relations defined by a pfst are closed under various operations such as union, concatenation, Kleene closure and composition.
		From a practical point of view, it is important to note that it is possible to adapt the constructions for classical transducers for pfst.
		The introduction of predicates over symbols is straightforward for operations such as union, concatenation, Kleene closure and cross-product.
	odur.let.rug.nl /vannoord/papers/preds/node19.html (80 words)

	Read about Kleene star at WorldVillage Encyclopedia. Research Kleene star and learn about Kleene star here! (Site not responding. Last check: 2007-10-11)
		computer science, the Kleene star (or Kleene closure) is a unary operation, either on sets of strings or on sets of symbols or characters.The application of the Kleene star to a set V is written as V*.
		regular expressions, which is the context in which it was introduced by Stephen Kleene to characterise certain
		The Kleene star is often generalized for any
	encyclopedia.worldvillage.com /s/b/Kleene_star (351 words)

	Encyclopedia: Kleene star
		Example of Kleene star applied to set of strings:
		Example of Kleene star applied to set of characters:
		The Kleene star is often generalized for any monoid (M,.), that is, a set M and binary operation '.' on M such that
	www.nationmaster.com /encyclopedia/Kleene-star (375 words)

	Regular Expressions and Recognizer Automata
		A Kleene closure expression matches zero or more concatenations of a subexpression.
		The class of regular expressions matching the Kleene closure of a regular expression.
		Closure nodes are nullable, since they represent zero or more repetitions.
	monday.sourceforge.net /lib/language/regular/regular.html (2127 words)

	KLEENE STAR
		(Or "Kleene closure", named after Stephen Kleene) The postfix "*" operator used in regular expressions, Extended Backus-Naur Form, and similar formalisms to specify a match for zero or more occurrences of the preceding expression.
		Source: compiled by the editor from various references; see credits.
		Specialty definitions using "KLEENE STAR": Kleene closure ♦ Stephen Kleene.
	www.websters-online-dictionary.org /Kl/Kleene+star.html (568 words)

	Kleene star -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-11)
		Kleene star -- Facts, Info, and Encyclopedia article
		It is widely used for (Click link for more info and facts about regular expressions) regular expressions, which is the context in which it was introduced by (Click link for more info and facts about Stephen Kleene) Stephen Kleene to characterise certain (Click link for more info and facts about automata) automata.
		The Kleene star is often generalized for any (Click link for more info and facts about monoid) monoid (M,.), that is, a set M and binary operation '.' on M such that
	www.absoluteastronomy.com /encyclopedia/K/Kl/Kleene_star.htm (356 words)

	► » Kleene closure of language and topology (Site not responding. Last check: 2007-10-11)
		► » Kleene closure of language and topology
		Subject: Re: Kleene closure of language and topology
		applying the Kleen star operator on a language is a topological space.
	www.science-chat.org /Kleene-closure-of-language-and-topology-6884630.html (408 words)

	CMSC 451 Selected Lecture Notes
		The epsilon closure is the initial state and all states that can be reached by one or more epsilon moves.
		The initial state of our new machine is {q0,q1,q2} the epsilon closure of q0 The final state(s) of our new machine is the new state(s) that contain a state symbol that was a final state in the original machine.
		Concatenation, union and Kleene star are constructed using the corresponding regular expression to NFA technique.
	www.cs.umbc.edu /~squire/s01-451/cs451_lect.html (9721 words)

	[No title]
		Regular languages Closure properties (are regular languages closed under...) 1.
		CFG closure properties (are CFGs closed under...) 1.
		Classifying languages It is important to be able to classify languages as regular, context-free, recursive, or recursively enumerable.
	www-cse.ucsd.edu /~vogt/comps/THEORY/GEORGETHEORYNOTES (918 words)

	97-61: Arithmetic Complexity, Kleene Closure, and Formal Power Series (Site not responding. Last check: 2007-10-11)
		GapL is the complexity class that characterizes the complexity of computing the determinant; it corresponds to counting the number of accepting and rejecting paths of nondeterministic logspace-bounded Turing machines.) We define a counting version of Kleene closure and show that it is intimately related to inversion within the complexity classes GapL and GapNC^1.
		There is a set in AC^0 for which Kleene closure is NL-complete and inversion is GapL-complete.
		Furthermore, we classify the complexity of the Kleene closure of finite languages.
	dimacs.rutgers.edu /TechnicalReports/abstracts/1997/97-61.html (204 words)

	Reduction rule for Kleene's Closure in replacement of Thompson's algorit (Site not responding. Last check: 2007-10-11)
		Reduction rule for Kleene's Closure in replacement of Thompson's algorit
		Reduction rule for Kleene's Closure in replacement of Thompson's algorithm
		I hope I now finally found the way I was looking for, to formulate a reduction rule for Kleene's Closure which can be used in replacement of Thompson's algorithm, or so I hope.
	www.archivum.info /gcc@gcc.gnu.org/2005-05/msg00687.html (186 words)

	ECCC Report TR99-008 and related Papers (Site not responding. Last check: 2007-10-11)
		We define a counting version of Kleene closure and show that it is intimately related to inversion and root extraction within GapNC^1 and GapL.
		We prove that Kleene closure, inversion, and root extraction are all hard operations in the following sense: There is a language in AC^0 for which inversion and root extraction are GapL-complete, and there is a finite set for which inversion and root extraction are GapNC^1- complete, with respect to appropriate reducibilities.
		We formulate the problem in terms of finite monoids and relate its complexity to the internal structure of the monoid.
	www.eccc.uni-trier.de /eccc-reports/1999/TR99-008 (273 words)

	Properties of Regular Languages (Site not responding. Last check: 2007-10-11)
		If we apply the operations of concatenation and Kleene closure, as well as the basic set theoretic operations of union, intersection and complementation to any (pair of) regular languages, the result will always be a regular language, too.
		We will discuss why this is so, and see how we can construct automata for the languages resulting from these operations based on the one(s) for the respective input language(s).
		The set of regular languages is closed under concatenation, union and Kleene closure.
	www.coli.uni-saarland.de /projects/milca/courses/coal/xhtml/REGULARLANGUAGES.SEC.PROPERTIES.xhtml (228 words)

	Arithmetic Complexity, Kleene Closure, and Formal Power Series (ResearchIndex) (Site not responding. Last check: 2007-10-11)
		Abstract: The aim of this paper is to use formal power series techniques to study the structure of small arithmetic complexity classes such as GapNC and GapL.
		We define a counting version of Kleene closure and show that it is intimately related to inversion and root extraction within GapNC and GapL.
		We prove that Kleene closure, inversion, and root extraction are all hard...
	citeseer.csail.mit.edu /689576.html (763 words)

	Arithmetic Complexity, Kleene Closure, and Formal Power Series (ResearchIndex) (Site not responding. Last check: 2007-10-11)
		Abstract: The aim of this paper is to use formal power series techniques to study the structure of small arithmetic complexity classes such as GapNC 1 and GapL.
		More precisely, we apply the Kleene closure of languages and the formal power series operations of inversion and root extraction to these complexity classes.
		We define a counting version of Kleene closure and show that it is intimately related to inversion and root extraction within GapNC 1 and GapL.
	citeseer.ist.psu.edu /128914.html (618 words)

	Kleene star from LiveJournal (Site not responding. Last check: 2007-10-11)
		The Kleene star consists of all strings which can be written in the form w1w2...wn with strings wi in L1 and.
		The kleene star is a mathematical operator which means "to do something zero or more times." I picked the name back when I was a big theoretical computer-science geek and thought the kleene star was the most...
		The asterisk means Kleene Star which stands for any number of the objects being starred.
	www.ljseek.com /search/Kleene%20star (619 words)

	CAVE Demo Page (Site not responding. Last check: 2007-10-11)
		It is intended to serve as a teaching tool for computer theory instructors and students.
		Three of these constructive algorithms (union, product, and Kleene closure) are used in the proof of Kleene's theorem.
		Kleene's theorem states that finite-state automata, transition graphs, and regular languages are equivalent in terms of their expressive power.
	www.cs.virginia.edu /~mst2f/cave.html (547 words)

	[No title]
		The set N of natural numbers are countably infinite.
		Theorem: the set of regular languages is closed under union, (set) concatenation, Kleene closure (star), regular substitution, and homomorphism.
		The cardinality of a finite set is the number of elements in the set, also called size.
	www.cs.uiowa.edu /~hzhang/c135/week1.ppt (399 words)

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