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230
A characterization of substitutive sequences using return words. Discrete Mathematics
, 1998
"... We prove that a sequence is primitive substitutive if and only if the set of its derived sequences is finite; we defined these sequences here. ..."
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Cited by 66 (10 self)
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We prove that a sequence is primitive substitutive if and only if the set of its derived sequences is finite; we defined these sequences here.
The Nondeterministic Complexity of a Finite Automaton
, 1990
"... We define the nondeterministic complexity of a finite automaton and show that there exist, for any integer p>=1, automata which need \Theta(k^{1/p}) nondeterministic transitions to spell words of length k. This leads to a subdivision of the family of recognizable Msubsets of a free monoid into a ..."
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Cited by 28 (2 self)
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We define the nondeterministic complexity of a finite automaton and show that there exist, for any integer p>=1, automata which need \Theta(k^{1/p}) nondeterministic transitions to spell words of length k. This leads to a subdivision of the family of recognizable Msubsets of a free monoid into a hierarchy whose members are indexed by polynomials, where M denotes the MinPlus semiring.
Symbolic Dynamics and Finite Automata
, 1999
"... this paper, based on notes by R. Beals and M. Spivak, methods of nite semigroups were introduced to obtain some of the results of G. Hedlund. ..."
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Cited by 26 (9 self)
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this paper, based on notes by R. Beals and M. Spivak, methods of nite semigroups were introduced to obtain some of the results of G. Hedlund.
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 25 (9 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
Coding properties of DNA languages
 In: Theoretical Computer Science
, 2002
"... The computation language of a DNAbased system consists of all the words (DNA strands) that can appear in any computation step of the system. In this work we define properties of languages which ensure that the words of such languages will not form undesirable bonds when used in DNA computations ..."
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Cited by 21 (10 self)
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The computation language of a DNAbased system consists of all the words (DNA strands) that can appear in any computation step of the system. In this work we define properties of languages which ensure that the words of such languages will not form undesirable bonds when used in DNA computations. We give several characterizations of the desired properties and provide methods for obtaining languages with such properties. The decidability of these properties is addressed as well. As an application we consider splicing systems whose computation language is free of certain undesirable bonds and is generated by nearly optimal commafree codes. 1 Introduction DNA (deoxyribonucleic acid) is found in every cellular organism as the storage medium for genetic information. It is composed of units called nucleotides, distinguished by the chemical group, or base, attached to them. The four bases, are adenine, guanine, cytosine and thymine, abbreviated as A, G, C, and T . (The names of th...
The groups of Richard Thompson and complexity
 International Conference on Semigroups and Groups in honor of the 65th birthday of Prof
, 2004
"... We prove new results about the remarkable infinite simple groups introduced by Richard Thompson in the 1960s. We define the groups as partial transformation groups and we give a faithful representation in the Cuntz C ⋆algebra. For the finitely presented simple group Tfin we show that the wordlengt ..."
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Cited by 17 (7 self)
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We prove new results about the remarkable infinite simple groups introduced by Richard Thompson in the 1960s. We define the groups as partial transformation groups and we give a faithful representation in the Cuntz C ⋆algebra. For the finitely presented simple group Tfin we show that the wordlength and the table size satisfy an n log n relation, just like the symmetric groups. We show that the word problem of Tfin belongs to the parallel complexity class AC 1 (a subclass of P). We show that the generalized word problem of Tfin is undecidable. We study the distortion functions of Tfin and we show that Tfin contains all finite direct products of finitely generated free groups as subgroups with linear distortion. As a consequence, up to polynomial equivalence of functions, the following three sets are the same: the set of distortions of Tfin, the set of all Dehn functions of finitely presented groups, and the set of time complexity functions of nondeterministic Turing machines. 1
Partial Words for DNA Coding
 In Preliminary Proceedings of 10th International Workshop on DNABased Computers, DNA 2004 (University of MilanoBicocca
, 2004
"... A very basic problem in all DNA computations is nding a good encoding. Apart from the fact that they must provide a solution, the strands involved should not exhibit any undesired behaviour like forming secondary structures. ..."
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Cited by 16 (1 self)
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A very basic problem in all DNA computations is nding a good encoding. Apart from the fact that they must provide a solution, the strands involved should not exhibit any undesired behaviour like forming secondary structures.
The Expressibility of Languages and Relations By Word Equations
, 1997
"... Classically, several properties and relations of words, such as "being a power of a same word", can be expressed by using word equations. This paper is devoted to study in general the expressive power of word equations. As main results we prove theorems which allow us to show that certain ..."
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Cited by 15 (6 self)
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Classically, several properties and relations of words, such as "being a power of a same word", can be expressed by using word equations. This paper is devoted to study in general the expressive power of word equations. As main results we prove theorems which allow us to show that certain properties of words are not expressible as components of solutions of word equations. In particular, "the primitiveness" and "the equal length" are such properties, as well as being "any word over a proper subalphabet".
Language equations, maximality and errordetection
, 2005
"... We use some ‘natural’ language operations, such as shuffle (scattered insertion) and scattered deletion to model noisy channels, that is, nondeterministic processes transforming words to words. In this spirit, we also introduce the operation of scattered substitution and derive the closure propertie ..."
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Cited by 13 (7 self)
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We use some ‘natural’ language operations, such as shuffle (scattered insertion) and scattered deletion to model noisy channels, that is, nondeterministic processes transforming words to words. In this spirit, we also introduce the operation of scattered substitution and derive the closure properties of the language families in the Chomsky hierarchy under this operation. Moreover, we consider a certain type of language inequations involving language operations and observe that, by varying the parameters of such an inequation, we can define families of codes such as prefix and infix, as well as families of errordetecting languages. Our results on this type of inequations include a characterization of the maximal solutions, which provides a uniform method for deciding whether a given regular code of the type defined by the inequation is maximal.