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146
Finding approximate repetitions under Hamming distance
 THEORETICAL COMPUTER SCIENCE
, 2001
"... The problem of computing tandem repetitions with K possible mismatches is studied. Two main definitions are considered, and for both of them an O(nK log K + S) algorithm is proposed (S the size of the output). This improves, in particular, the bound obtained in [LS93]. Finally, other possible defini ..."
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Cited by 36 (1 self)
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The problem of computing tandem repetitions with K possible mismatches is studied. Two main definitions are considered, and for both of them an O(nK log K + S) algorithm is proposed (S the size of the output). This improves, in particular, the bound obtained in [LS93]. Finally, other possible definions are briefly analyzed.
The Monadic Theory of Morphic Infinite Words and Generalizations
"... We present new examples of infinite words which have a decidable monadic theory. Formally, we consider structures hN; <; P i which expand the ordering hN; <i of the natural numbers by a unary predicate P ; the corresponding infinite word is the characteristic 01sequence xP of P . We show tha ..."
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Cited by 31 (7 self)
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We present new examples of infinite words which have a decidable monadic theory. Formally, we consider structures hN; <; P i which expand the ordering hN; <i of the natural numbers by a unary predicate P ; the corresponding infinite word is the characteristic 01sequence xP of P . We show that for a morphic predicate P the associated monadic secondorder theory MThhN; <; P i is decidable, thus extending results of Elgot and Rabin (1966) and Maes (1999). The solution is obtained in the framework of semigroup theory, which is then connected to the known automata theoretic approach of Elgot and Rabin. Finally, a large class of predicates P is exhibited such that the monadic theory MThhN; <; P i is decidable, which unifies and extends the previously known examples.
Periodicity on Partial Words
 Computers and Mathematics with Applications 47
, 2004
"... Codes play an important role in the study of combinatorics on words. Recently, we introduced pcodes that play a role in the study of combinatorics on partial words. Partial words are strings over a finite alphabet that may contain a number of “do not know ” symbols. In this paper, the theory of code ..."
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Cited by 30 (12 self)
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Codes play an important role in the study of combinatorics on words. Recently, we introduced pcodes that play a role in the study of combinatorics on partial words. Partial words are strings over a finite alphabet that may contain a number of “do not know ” symbols. In this paper, the theory of codes of words is revisited starting from pcodes of partial words. We present some important properties of pcodes. We give several equivalent definitions of pcodes and the monoids they generate. We investigate in particular the Defect Theorem for partial words. We describe an algorithm to test whether or not a finite set of partial words is a pcode. We also discuss twoelement pcodes, complete pcodes, maximal pcodes, and the class of circular pcodes. A World Wide Web server interface has been established at
Polynomial versus exponential growth in repetitionfree words
 J. Comb. Th. A
, 2004
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Combinatorics of Periods in Strings
"... We consider the set (n) of all period sets of strings of length n over a nite alphabet. We show that there is redundancy in period sets and introduce the notion of an irreducible period set. We prove that (n) is a lattice under set inclusion and does not satisfy the JordanDedekind condition. We ..."
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Cited by 22 (4 self)
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We consider the set (n) of all period sets of strings of length n over a nite alphabet. We show that there is redundancy in period sets and introduce the notion of an irreducible period set. We prove that (n) is a lattice under set inclusion and does not satisfy the JordanDedekind condition. We propose the rst enumeration algorithm for (n) and improve upon the previously known asymptotic lower bounds on the cardinality of (n). Finally, we provide a new recurrence to compute the number of strings sharing a given period set. 1
On a Special Class of Primitive Words
"... Abstract. When representing DNA molecules as words, it is necessary to take into account the fact that a word u encodes basically the same information as its WatsonCrick complement θ(u), where θ denotes the WatsonCrick complementarity function. Thus, an expression which involves only a word u and ..."
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Cited by 19 (14 self)
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Abstract. When representing DNA molecules as words, it is necessary to take into account the fact that a word u encodes basically the same information as its WatsonCrick complement θ(u), where θ denotes the WatsonCrick complementarity function. Thus, an expression which involves only a word u and its complement can be still considered as a repeating sequence. In this context, we define and investigate the properties of a special class of primitive words, called θprimitive, which cannot be expressed as such repeating sequences. For instance, we prove the existence of a unique θprimitive root of a given word, and we give some constraints forcing two distinct words to share their θprimitive root. Also, we present an extension of the wellknown Fine and Wilf Theorem, for which we give an optimal bound. 1
A discontinuity in pattern inference
 In Proceedings of the 21st Symposium on Theoretical Aspects of Computer Science, STACS 2004
, 2004
"... A discontinuity in pattern inference This item was submitted to Loughborough University’s Institutional Repository by the/an author. ..."
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Cited by 19 (11 self)
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A discontinuity in pattern inference This item was submitted to Loughborough University’s Institutional Repository by the/an author.
Periods and Binary Words
 J. Combin. Theory Ser. A
, 2000
"... We give an elementary short proof for a wellknown theorem of Guibas and Odlyzko stating that the sets of periods of words are independent of the alphabet size. As a consequence of our constructing proof, we give a linear time algorithm which, given a word, computes a binary one with the same period ..."
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Cited by 18 (6 self)
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We give an elementary short proof for a wellknown theorem of Guibas and Odlyzko stating that the sets of periods of words are independent of the alphabet size. As a consequence of our constructing proof, we give a linear time algorithm which, given a word, computes a binary one with the same periods. We give also a very short proof for the famous Fine and Wilf's periodicity lemma.
Local periods and binary partial words: an algorithm, Theoretical Computer Science 314
, 2004
"... The study of the combinatorial properties of strings of symbols from a finite alphabet (also referred to as words) is profoundly connected to numerous fields such as biology, computer science, mathematics, and physics. Research in combinatorics on words goes back roughly a century. There is a renew ..."
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Cited by 17 (9 self)
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The study of the combinatorial properties of strings of symbols from a finite alphabet (also referred to as words) is profoundly connected to numerous fields such as biology, computer science, mathematics, and physics. Research in combinatorics on words goes back roughly a century. There is a renewed interest in combinatorics on words as a result of emerging new application areas such as molecular biology. Partial words were recently introduced in this context. The motivation behind the notion of a partial word is the comparison of genes (or proteins). Alignment of two genes (or two proteins) can be viewed as a construction of partial words that are said to be compatible. While a word can be described by a total function, a partial word can be described by a partial function. More precisely, a partial word of length n over a finite alphabet A is a partial function from {1,..., n} into A. Elements of {1,..., n} without an image are called holes. A word is just a partial word without holes. The notion of period of a word is central in combinatorics on words. In the case of partial words, there are two notions: one is that of period, the other is that of local period.