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What (who) is K-synchronized sequence - definition
K-synchronized sequence
In mathematics and theoretical computer science, a k-synchronized sequence is an infinite sequence of terms s(n) characterized by a finite automaton taking as input two strings m and n, each expressed in some fixed base k, and accepting if m = s(n). The class of k-synchronized sequences lies between the classes of k-automatic sequences and k-regular sequences.
Automatic sequence
AN INFINITE SEQUENCE OF TERMS CHARACTERIZED BY A FINITE AUTOMATON
Automatic set; Automatic real number; Period-doubling sequence; Cobham–Semenov theorem; K-automatic sequence; Cobham-Semenov theorem; Automatic sequences
In mathematics and theoretical computer science, an automatic sequence (also called a k-automatic sequence or a k-recognizable sequence when one wants to indicate that the base of the numerals used is k) is an infinite sequence of terms characterized by a finite automaton. The n-th term of an automatic sequence a(n) is a mapping of the final state reached in a finite automaton accepting the digits of the number n in some fixed base k.
Sequence (music)
![Cello Suite]] in G, BWV 1007](https://commons.wikimedia.org/wiki/Special:FilePath/Bach Prelude from Cello Suite in G.png?width=200 "Cello Suite]] in G, BWV 1007")
![Concerto for Two Violins]] in D minor, first movement, bars 22-24](https://commons.wikimedia.org/wiki/Special:FilePath/J.S. Bach Concerto for Two Violins in D minor, first movement, bars 22-24.png?width=200 "Concerto for Two Violins]] in D minor, first movement, bars 22-24")
![Mozart]] Minuet in F K6](https://commons.wikimedia.org/wiki/Special:FilePath/Mozart Minuet in F K6.png?width=200 "Mozart]] Minuet in F K6")
![Opening bars of "[[The Star-Spangled Banner]]"](https://commons.wikimedia.org/wiki/Special:FilePath/Star-spagled Banner opening bars.png?width=200 "Opening bars of \"[[The Star-Spangled Banner]]\"")
IMMEDIATE RESTATEMENT OF A MOTIF AT A HIGHER OR LOWER PITCH IN THE SAME VOICE
Modulating sequence; Real sequence; Tonal sequence; Modified sequence; False sequence; Descending fifths sequence; Rhythmic sequence
. Note that there are only four segments, continuingly higher, and that the segments continue by similar distance (seconds: C-D, D-E, etc.
