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Advances in Mathematics: Scientific Journal, 2020
Partial words are linear words with holes. Cyclic words are derived from linear words by linking its first letter after the last one. Both partial words and cyclic words have wide applications in DNA sequencing. In this paper we introduce cyclic partial words and discuss their periodicity and certain properties.
R.K. Kumari +3 more
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Partial words are linear words with holes. Cyclic words are derived from linear words by linking its first letter after the last one. Both partial words and cyclic words have wide applications in DNA sequencing. In this paper we introduce cyclic partial words and discuss their periodicity and certain properties.
R.K. Kumari +3 more
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2013
Recently, Dassow et al. connected partial words and regular languages. Partial words are sequences in which some positions may be undefined, represented with a "hole" symbol ⋄. If we restrict what the symbol ⋄ can represent, we can use partial words to compress the representation of regular languages.
Eric Balkanski +3 more
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Recently, Dassow et al. connected partial words and regular languages. Partial words are sequences in which some positions may be undefined, represented with a "hole" symbol ⋄. If we restrict what the symbol ⋄ can represent, we can use partial words to compress the representation of regular languages.
Eric Balkanski +3 more
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2007
Partial words are strings over a finite alphabet that may contain a number of "do not know" symbols. In this paper, we introduce the notions of binary and ternary correlations, which are binary and ternary vectors indicating the periods and weak periods of partial words. Extending a result of Guibas and Odlyzko, we characterize precisely which of these
Francine Blanchet-Sadri +2 more
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Partial words are strings over a finite alphabet that may contain a number of "do not know" symbols. In this paper, we introduce the notions of binary and ternary correlations, which are binary and ternary vectors indicating the periods and weak periods of partial words. Extending a result of Guibas and Odlyzko, we characterize precisely which of these
Francine Blanchet-Sadri +2 more
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ALGORITHMIC COMBINATORICS ON PARTIAL WORDS
International Journal of Foundations of Computer Science, 2012Algorithmic combinatorics on partial words, or sequences of symbols over a finite alphabet that may have some do-not-know symbols or holes, has been developing in the past few years. Applications can be found, for instance, in molecular biology for the sequencing and analysis of DNA, in bio-inspired computing where partial words have been considered ...
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Avoidable Binary Patterns in Partial Words
Acta Informatica, 2010The classification of all binary patterns according to partial word avoidability is obtained in this very interesting paper. A new terminology on unavoidable patterns is introduced in order to include some undefined positions called holes. Using iterated morphisms, the construction of binary partial words with infinitely many holes avoiding certain ...
Blanchet-Sadri, F. +3 more
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Counting Primitive Partial Words
2010A word is primitive if it is not a power of another word. The number of primitive words of a fixed length over an alphabet of a fixed size is well known and relates to the Möbius function. In this paper, we investigate the number of primitive partial words which are strings that may contain "do not know" symbols.
Blanchet-Sadri, Francine +1 more
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2017
In DNA computing experiments, it is important that the strands involved in the computation do not interact in an undesirable fashion. The mathematical formalization of the DNA WK-complementarity as an antimorphic involution, has motivated the generalization of various concepts in combinatorics of words to ones that involve pseudo-identity functions ...
Manasi S. Kulkarni +2 more
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In DNA computing experiments, it is important that the strands involved in the computation do not interact in an undesirable fashion. The mathematical formalization of the DNA WK-complementarity as an antimorphic involution, has motivated the generalization of various concepts in combinatorics of words to ones that involve pseudo-identity functions ...
Manasi S. Kulkarni +2 more
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Squares in Binary Partial Words
2012In this paper, we investigate the number of positions that do not start a square, the number of square occurrences, and the number of distinct squares in binary partial words. Letting σh(n) be the maximum number of positions not starting a square for binary partial words with h holes of length n, we show that limσh(n)/n=15/31 provided the limit of h/n ...
Francine Blanchet-Sadri +2 more
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Abelian Square-Free Partial Words
2010Erdos raised the question whether there exist infinite abelian square-free words over a given alphabet (words in which no two adjacent subwords are permutations of each other). Infinite abelian square-free words have been constructed over alphabets of sizes as small as four.
Francine Blanchet-Sadri +4 more
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2005
A very basic problem in all DNA computations is finding a good encoding. Apart from the fact that they must provide a solution, the strands involved should not exhibit any undesired behaviour, especially they should not form secondary structures. Various combinatorial properties like repetition-freeness and involution-freeness have been proposed to ...
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A very basic problem in all DNA computations is finding a good encoding. Apart from the fact that they must provide a solution, the strands involved should not exhibit any undesired behaviour, especially they should not form secondary structures. Various combinatorial properties like repetition-freeness and involution-freeness have been proposed to ...
openaire +1 more source