Disjunctive sequence

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 p_S(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.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Disjunctive_sequence

Lexicon (disambiguation)

The lexicon of a language is its vocabulary.

Lexicon is also a synonym for a dictionary or encyclopedic dictionary, and may also refer to:

Lexicon (cardgame), a word card game of the 1930s

Lexicon (company), an audio equipment manufacturer

Lexicon Branding, a company devoted to inventing names for products

Lexicon Pharmaceuticals, a biopharmaceutical company

Lexicon (game), a role-playing game using Wiki software

Lexicon Gaming Convention, held in Lexington, Kentucky, USA

Lexicon (mathematics), a real number that is disjunctive to every base

Lexicon (novel), a 2013 novel by Max Barry

Lexicon (program), a text editor and word processor

Lexicon (typeface), a typeface designed by Bram de Does

Lexicon, the home planet of WordGirl, star of an educational TV show

DLR Lexicon, a building in Dún Laoghaire, Ireland

Lex Icon, a stage name used by Norwegian black metal musician Stian Arnesen (AKA Nagash)

Lexicon (game)

Lexicon is a computer-assisted role-playing game invented by Neel Krishnaswami and popularised by the indie role-playing game community. As originally proposed, it is played online using wiki software. Players assume the role of scholars who write the history and background of a particular fictitious time, setting, or incident. As the game goes on, the players collaboratively create an elaborately interwoven account.

Each game is a series of 26 turns, keyed to the letters of the alphabet from A to Z. On the first turn, each player must write an Encyclopedia-style entry beginning with the letter A, citing and linking to two entries that are not yet written. These are called "undefined" entries. Undefined entries must begin with a letter later in the alphabet.

The 25 subsequent turns proceed consecutively through the letters of the alphabet, one letter per turn. In a turn, each player writes one entry that begins with the turn's specified letter. If one or more undefined entries are available that begin with the letter, a player must choose and write an undefined entry before any new entries can be created under that letter. A new entry must create and link to two undefined entries, and must also link to an entry written on a previous turn. Near the endgame, when sufficient undefined entries exist to occupy all players for the remainder of the game, no new undefined entries may be created.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Lexicon_(game)