scholarly journals The Maximal Subword Complexity of Quasiperiodic Infinite Words

2010 ◽  
Vol 31 ◽  
pp. 169-176 ◽  
Author(s):  
Ronny Polley ◽  
Ludwig Staiger
Keyword(s):  
Infinite Words ◽  
Subword Complexity

scholarly journals Infinite words with linear subword complexity

1989 ◽  
Vol 65 (2) ◽  
pp. 221-242 ◽  
Author(s):  
Filippo Mignosi
Keyword(s):  
Infinite Words ◽  
Subword Complexity

scholarly journals WORD COMPLEXITY AND REPETITIONS IN WORDS

2004 ◽  
Vol 15 (01) ◽  
pp. 41-55 ◽  
Author(s):  
LUCIAN ILIE ◽  
SHENG YU ◽  
KAIZHONG ZHANG
Keyword(s):  
Data Compression ◽  
Fast Algorithms ◽  
Complexity Measure ◽  
Combinatorics On Words ◽  
Complexity Measures ◽  
Infinite Words ◽  
Infinite Word ◽  
De Bruijn ◽  
Subword Complexity

With ideas from data compression and combinatorics on words, we introduce a complexity measure for words, called repetition complexity, which quantifies the amount of repetition in a word. The repetition complexity of w, R (w), is defined as the smallest amount of space needed to store w when reduced by repeatedly applying the following procedure: n consecutive occurrences uu…u of the same subword u of w are stored as (u,n). The repetition complexity has interesting relations with well-known complexity measures, such as subword complexity, SUB , and Lempel-Ziv complexity, LZ . We have always R (w)≥ LZ (w) and could even be that the former is linear while the latter is only logarithmic; e.g., this happens for prefixes of certain infinite words obtained by iterated morphisms. An infinite word α being ultimately periodic is equivalent to: (i) [Formula: see text], (ii) [Formula: see text], and (iii) [Formula: see text]. De Bruijn words, well known for their high subword complexity, are shown to have almost highest repetition complexity; the precise complexity remains open. R (w) can be computed in time [Formula: see text] and it is open, and probably very difficult, to find fast algorithms.

Fuzzy regular languages over finite and infinite words

2006 ◽  
Vol 157 (11) ◽  
pp. 1532-1549 ◽  
Author(s):  
Werner Kuich ◽  
George Rahonis
Keyword(s):  
Regular Languages ◽  
Infinite Words

scholarly journals On subword complexity functions

1984 ◽  
Vol 8 (2) ◽  
pp. 209-212 ◽  
Author(s):  
Anni Sajo
Keyword(s):  
Subword Complexity

scholarly journals Quasi-periodic configurations and undecidable dynamics for tilings, infinite words and Turing machines

2004 ◽  
Vol 319 (1-3) ◽  
pp. 127-143 ◽  
Author(s):  
Jean-Charles Delvenne ◽  
Vincent D. Blondel
Keyword(s):  
Turing Machines ◽  
Infinite Words

Infinite Words and a Problem in Semigroup Theory

Sequences ◽  
1990 ◽  
pp. 254-257
Author(s):  
Jacques Justin ◽  
Giuseppe Pirillo
Keyword(s):  
Semigroup Theory ◽  
Infinite Words

scholarly journals An Inequality for the Number of Periods in a Word

2021 ◽  
pp. 1-18
Author(s):  
Daniel Gabric ◽  
Narad Rampersad ◽  
Jeffrey Shallit
Keyword(s):  
Critical Exponent ◽  
Infinite Words ◽  
Sturmian Word ◽  
Special Cases

We prove an inequality for the number of periods in a word [Formula: see text] in terms of the length of [Formula: see text] and its initial critical exponent. Next, we characterize all periods of the length-[Formula: see text] prefix of a characteristic Sturmian word in terms of the lazy Ostrowski representation of [Formula: see text], and use this result to show that our inequality is tight for infinitely many words [Formula: see text]. We propose two related measures of periodicity for infinite words. Finally, we also consider special cases where [Formula: see text] is overlap-free or squarefree.

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