About: Disjunctive sequence

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Disjunctive sequence Goto Sponge NotDistinct Permalink

An Entity of Type : yago:Series108457976, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FDisjunctive_sequence&invfp=IFP_OFF&sas=SAME_AS_OFF

A disjunctive sequence is an infinite sequence (over a finite alphabet of characters) in which every finite string appears as a substring. For instance, the binary Champernowne sequence formed by concatenating all binary strings in shortlex order, clearly contains all the binary strings and so is disjunctive. (The spaces above are not significant and are present solely to make clear the boundaries between strings). The complexity function of a disjunctive sequence S over an alphabet of size k is pS(n) = kn. A disjunctive sequence is recurrent but never uniformly recurrent/almost periodic.

Attributes	Values
rdf:type	yago:WikicatSequencesAndSeries yago:Abstraction100002137 yago:Arrangement107938773 yago:Group100031264 yago:Ordering108456993 yago:Sequence108459252 yago:Series108457976
rdfs:label	Disjunctive sequence (en) Nombre univers (fr)
rdfs:comment	A disjunctive sequence is an infinite sequence (over a finite alphabet of characters) in which every finite string appears as a substring. For instance, the binary Champernowne sequence formed by concatenating all binary strings in shortlex order, clearly contains all the binary strings and so is disjunctive. (The spaces above are not significant and are present solely to make clear the boundaries between strings). The complexity function of a disjunctive sequence S over an alphabet of size k is pS(n) = kn. A disjunctive sequence is recurrent but never uniformly recurrent/almost periodic. (en) Un nombre univers est un nombre réel dans les décimales duquel on peut trouver n'importe quelle succession de chiffres de longueur finie, pour une base donnée. Ainsi, si l'on se donne une manière de coder les caractères d'un livre selon une suite de chiffres (ce qui est le cas, par exemple, dans tout format informatique), on trouvera dans un nombre univers tous les livres déjà écrits et à venir, y compris celui de l'histoire de votre vie passée et future. (fr)
dct:subject	Sequences and series
Wikipage page ID	4251950 (xsd:integer)
Wikipage revision ID	1032027967 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Prime number theorem Sequences and series Character (computing) Limit of a sequence Comeager Alphabet (computer science) Complexity function Dense set String (computer science) Shortlex order Cube (algebra) Floor and ceiling functions Normal number Conversion (logic) Radix Prime number Pi Polynomial Square numbers Natural numbers Real number Champernowne constant Sequence Unit interval Recurrent word Substring Euler's number
sameAs	Disjunctive sequence Disjunctive sequence Disjunctive sequence Disjunctive sequence Disjunctive sequence
dbp:wikiPageUsesTemplate	dbt:Anchor dbt:Cite_book dbt:Cite_journal dbt:Mono dbt:Refbegin dbt:Refend dbt:Reflist
has abstract	A disjunctive sequence is an infinite sequence (over a finite alphabet of characters) in which every finite string appears as a substring. For instance, the binary Champernowne sequence formed by concatenating all binary strings in shortlex order, clearly contains all the binary strings and so is disjunctive. (The spaces above are not significant and are present solely to make clear the boundaries between strings). The complexity function of a disjunctive sequence S over an alphabet of size k is pS(n) = kn. Any normal sequence (a sequence in which each string of equal length appears with equal frequency) is disjunctive, but the converse is not true. For example, letting 0n denote the string of length n consisting of all 0s, consider the sequence obtained by splicing exponentially long strings of 0s into the shortlex ordering of all binary strings. Most of this sequence consists of long runs of 0s, and so it is not normal, but it is still disjunctive. A disjunctive sequence is recurrent but never uniformly recurrent/almost periodic. (en) Un nombre univers est un nombre réel dans les décimales duquel on peut trouver n'importe quelle succession de chiffres de longueur finie, pour une base donnée. Ainsi, si l'on se donne une manière de coder les caractères d'un livre selon une suite de chiffres (ce qui est le cas, par exemple, dans tout format informatique), on trouvera dans un nombre univers tous les livres déjà écrits et à venir, y compris celui de l'histoire de votre vie passée et future. Mais on ne peut bien sûr pas en tirer une quelconque information : ce serait aussi efficace que de générer une succession aléatoire de lettres et de réessayer jusqu'à obtenir le livre que l'on cherche, et cela suppose de le connaître déjà lettre par lettre. (fr)
prov:wasDerivedFrom	wikipedia-en:Disjunctive_sequence?oldid=1032027967&ns=0
page length (characters) of wiki page	7912 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Disjunctive_sequence
is Link from a Wikipage to another Wikipage of	Lexicon (mathematics) Normal number Ehrenfeucht–Mycielski sequence Champernowne constant Disjunctive Disjunctive number Disjunctive word Rich number
is Wikipage redirect of	Lexicon (mathematics) Disjunctive number Disjunctive word Rich number
is Wikipage disambiguates of	Disjunctive
is foaf:primaryTopic of	wikipedia-en:Disjunctive_sequence

Faceted Search & Find service v1.17_git145 as of Aug 30 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3331 as of Sep 2 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 50 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software