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 words.

General Idempotency Languages Over Small Alphabets

“…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].…”

Reconstruction Codes for DNA Sequences With Uniform Tandem-Duplication Errors

“…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).…”

Duplication in DNA Sequences

“…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…”

“…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].…”