Kleene star
E601578
The Kleene star is a fundamental operation in formal language theory and regular expressions that denotes the set of all finite concatenations (including the empty string) of a given symbol or pattern.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Kleene star canonical | 6 |
| Kleene closure | 1 |
| Kleene star in formal language theory | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6594123 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Kleene star Context triple: [Stephen Kleene, knownFor, Kleene star]
-
A.
Chomsky hierarchy
The Chomsky hierarchy is a classification of formal grammars into four types that correspond to increasing levels of generative power and computational complexity in formal language theory.
-
B.
Kleene numbering
Kleene numbering is a method in computability theory for effectively assigning natural numbers to partial recursive functions, refining Gödel numbering to study algorithmic properties of functions.
-
C.
Knuth’s up-arrow notation
Knuth’s up-arrow notation is a mathematical notation introduced by Donald Knuth to concisely represent very large integers using iterated exponentiation and its higher-order generalizations.
-
D.
Ackermann function
The Ackermann function is a classic example of a computable function that grows faster than any primitive recursive function, often used in theoretical computer science to illustrate extreme computational complexity.
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E.
Thompson's algorithm for regular expression matching
Thompson's algorithm for regular expression matching is a classic method that converts regular expressions into nondeterministic finite automata (NFAs) to enable efficient pattern matching in text processing.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Kleene star Target entity description: The Kleene star is a fundamental operation in formal language theory and regular expressions that denotes the set of all finite concatenations (including the empty string) of a given symbol or pattern.
-
A.
Chomsky hierarchy
The Chomsky hierarchy is a classification of formal grammars into four types that correspond to increasing levels of generative power and computational complexity in formal language theory.
-
B.
Kleene numbering
Kleene numbering is a method in computability theory for effectively assigning natural numbers to partial recursive functions, refining Gödel numbering to study algorithmic properties of functions.
-
C.
Knuth’s up-arrow notation
Knuth’s up-arrow notation is a mathematical notation introduced by Donald Knuth to concisely represent very large integers using iterated exponentiation and its higher-order generalizations.
-
D.
Ackermann function
The Ackermann function is a classic example of a computable function that grows faster than any primitive recursive function, often used in theoretical computer science to illustrate extreme computational complexity.
-
E.
Thompson's algorithm for regular expression matching
Thompson's algorithm for regular expression matching is a classic method that converts regular expressions into nondeterministic finite automata (NFAs) to enable efficient pattern matching in text processing.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
closure operator
ⓘ
operation in formal language theory ⓘ unary operator on sets of strings ⓘ |
| alsoKnownAs |
Kleene closure
ⓘ
linked to:
Kleene star
|
| appearsIn |
Kleene’s theorem on regular sets
ⓘ
definition of regular expressions ⓘ |
| closureProperty |
preserves context-freeness of languages
ⓘ
preserves regularity of languages ⓘ |
| codomain | sets of strings over the same alphabet ⓘ |
| differenceFrom | Kleene plus excludes the empty string ⓘ |
| domain | sets of strings over an alphabet ⓘ |
| example |
If L = {ab} then L* = {ε, ab, abab, ababab, …}
ⓘ
If L = {a} then L* = {ε, a, aa, aaa, …} ⓘ |
| field |
automata theory
ⓘ
formal language theory ⓘ mathematical logic ⓘ theoretical computer science ⓘ |
| formalDefinition | For a language L over an alphabet Σ, L* = ⋃_{n≥0} L^n ⓘ |
| includesEmptyString | true ⓘ |
| mathematicalStructure | idempotent with respect to application: (L*)* = L* ⓘ |
| namedAfter |
Stephen Cole Kleene
ⓘ
linked to:
Stephen Kleene
|
| notationInRegex | R* denotes zero or more repetitions of pattern R ⓘ |
| property |
(L*)* = L*
ⓘ
L* = {ε} ∪ L*·L ⓘ L* = {ε} ∪ L·L* ⓘ L* always contains the empty string ε ⓘ L* is infinite if L contains a non-empty string ⓘ L* is the smallest superset of L that is closed under concatenation and contains ε ⓘ if L is a regular language then L* is regular ⓘ if L is context-free then L* is context-free ⓘ {ε}* = {ε} ⓘ ∅* = {ε} ⓘ |
| relatedConcept | Kleene plus ⓘ |
| symbol | * ⓘ |
| usedIn |
Kleene algebra
ⓘ
compiler construction ⓘ finite automata ⓘ lexical analysis ⓘ pattern matching ⓘ program verification ⓘ regular expressions ⓘ regular languages ⓘ text processing ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Kleene star Description of subject: The Kleene star is a fundamental operation in formal language theory and regular expressions that denotes the set of all finite concatenations (including the empty string) of a given symbol or pattern.
Referenced by (8)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject linked to:
Kleene
linked to: Kleene star
linked to: Kleene star
subject linked to:
complexity class NL