About: Kleene star

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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. In mathematicsit is more commonly known as the free monoid construction. The application of the Kleene star to a set is written as . It is widely used for regular expressions, which is the context in which it was introduced by Stephen Kleene to characterize certain automata, where it means "zero or more repetitions". The operators are used in rewrite rules for generative grammars.

Attributes	Values
rdf:type	military conflict
rdfs:label	Kleene star (en)
rdfs:comment	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. In mathematicsit is more commonly known as the free monoid construction. The application of the Kleene star to a set is written as . It is widely used for regular expressions, which is the context in which it was introduced by Stephen Kleene to characterize certain automata, where it means "zero or more repetitions". The operators are used in rewrite rules for generative grammars. (en)
sameAs	Kleene star Kleene star
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Reflist dbt:Short_description dbt:Use_dmy_dates
Subject	Formal languages Grammar Natural language processing
gold:hypernym	Operation
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Kleene_star?oldid=1067284369&ns=0
Wikipage page ID	16750 (xsd:integer)
page length (characters) of wiki page	7178 (xsd:nonNegativeInteger)
Wikipage revision ID	1067284369 (xsd:integer)
Link from a Wikipage to another Wikipage	Formal language Unary operation Abstract family of languages Addison-Wesley Algebraic structure Associative property Automata theory Monoid Semiring Stephen Cole Kleene Wildcard character Free monoid Generative grammar Glob (programming) Formal languages Grammar Natural language processing Set (mathematics) Closure (mathematics) Commutative property Computer science Concatenation Countable set Rewriting Empty set Empty string Finite set Idempotence String (computer science) Subset Mathematical logic Regular expression
has abstract	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. In mathematicsit is more commonly known as the free monoid construction. The application of the Kleene star to a set is written as . It is widely used for regular expressions, which is the context in which it was introduced by Stephen Kleene to characterize certain automata, where it means "zero or more repetitions". 1. * If is a set of strings, then is defined as the smallest superset of that contains the empty string and is closed under the string concatenation operation. 2. * If is a set of symbols or characters, then is the set of all strings over symbols in , including the empty string . The set can also be described as the set containing the empty string and all finite-length strings that can be generated by concatenating arbitrary elements of , allowing the use of the same element multiple times. If is either the empty set ∅ or the singleton set , then ; if is any other finite set or countably infinite set, then is a countably infinite set. As a consequence, each formal language over a finite or countably infinite alphabet is countable, since it is a subset of the countably infinite set . The operators are used in rewrite rules for generative grammars. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Kleene_star
is Wikipage redirect of	Kleene closure Kleene operator Kleene operators Kleene plus Σ* Star closure Star operation
is Link from a Wikipage to another Wikipage of	Formal grammar Formal language Greibach's theorem Local language (formal language) NL (complexity) NP-completeness NP-completeness Noncommutative signal-flow graph Nondeterministic finite automaton AIXI Abstract family of languages Action algebra Algebraic structure Alphabet (formal languages) Arden's rule Asterisk Balanced ternary Monoidal category Brzozowski derivative Free monoid Free object Generalized star-height problem Glob (programming) History monoid Cyc Cyclic language List object List of formal language and literal string topics Closure (mathematics) Conjunctive grammar Constant-recursive sequence Context-free grammar Context-free language Context-sensitive grammar Context-free language Catalan number EXPSPACE List of computer scientists Ellipsis (computer programming) Embedded pushdown automaton Finite-state transducer Idempotence

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