2005
DOI: 10.1016/j.dam.2004.10.003
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Uniformly bounded duplication languages

Abstract: We consider a new type of language defined by a word through iterative factor duplications, inspired by the process of tandem repeats production in the evolution of DNA. We investigate the effect of restricting the factor length to a constant. We prove that all these languages are regular, any word has a unique uniformly bounded duplication root, and show how this root can be computed in linear time and memory. We also address the problem of computing the uniformly bounded duplication distance between two word… Show more

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Cited by 36 publications
(38 citation statements)
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“…For example for general duplication languages over bigger alphabets, it is till unknown whether they generate only context-free languages or also more complicated ones; only with a length restriction on the rules context-freeness has been proven [13].…”
Section: Idempotencies Generating Languagesmentioning
confidence: 99%
“…For example for general duplication languages over bigger alphabets, it is till unknown whether they generate only context-free languages or also more complicated ones; only with a length restriction on the rules context-freeness has been proven [13].…”
Section: Idempotencies Generating Languagesmentioning
confidence: 99%
“…We denote by Irr k the set of all irreducible words, and Irr k (n) Irr k ∩Z n q . It was shown in [20], [31] that for each word x ∈ Z k q , a unique irreducible word exists for which x is a descendant. We call it the root of x, and denote it by R k (x).…”
Section: Introductionmentioning
confidence: 99%
“…Note that this "controlled" duplication operation can express two variants of duplication that appear in previous literature ( [8], [9]), namely uniform and lengthbounded duplication. Indeed, using the notations in [8], we have…”
Section: Controlled Duplicationmentioning
confidence: 99%
“…Several properties of languages generated by duplication grammars were investigated in [12] and [13]. Another prevalent model for duplication is a unary operation on words [1], [2], [5], [7], [8], [9]. The biological phenomenon which motivates the research on duplication is a common error occurring during DNA replication: the insertion or deletion of repeated subsequences in DNA strands, [3].…”
Section: Introductionmentioning
confidence: 99%