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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 27 (14 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...
Substitutions on trajectories
, 2004
"... The word substitutions are binary word operations which can be basically interpreted as a deletion followed by insertion, with some restrictions applied. Besides being itself an interesting topic in formal language theory, they have been naturally applied to modelling noisy channels. We introduce ..."
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Cited by 3 (2 self)
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The word substitutions are binary word operations which can be basically interpreted as a deletion followed by insertion, with some restrictions applied. Besides being itself an interesting topic in formal language theory, they have been naturally applied to modelling noisy channels. We introduce the concept of substitution on trajectories which generalizes a class of substitution operations. Within this framework, we study their closure properties and decision questions related to language equations. We also discuss applications of substitution on trajectories in modelling complex channels and a cryptanalysis problem.
Transducers and the Properties of ErrorDetection, ErrorCorrection and FiniteDelay Decodability
 Journal of Universal Computer Science
"... Xρóνια πoλλ´α κ´υριε Γιo´υργκενσεν. E´υχoµαι να τα εκατoστ ´ησετε. Abstract: When the words of a language are communicated via a noisy channel, the language property of errordetection ensures that no word of the language can be transformed to another word of the language. On the other hand, the pro ..."
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Cited by 13 (9 self)
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Xρóνια πoλλ´α κ´υριε Γιo´υργκενσεν. E´υχoµαι να τα εκατoστ ´ησετε. Abstract: When the words of a language are communicated via a noisy channel, the language property of errordetection ensures that no word of the language can be transformed to another word of the language. On the other hand, the property of errorcorrection ensures that the channel cannot transform two different words of the language to the same word. In this work we use transducers to model noisy channels and consider a few simple transducer operations that can be used to reduce the language properties of errordetection and errorcorrection to the transducer property of functionality. As a consequence, we obtain simple polynomialtime algorithms for deciding these properties for regular languages. On the other hand the properties are not decidable for contextfree languages. In addition we show that, in a certain sense, the class of rational channels can be used to model various error combinations. Using the same tools, we also obtain simple polynomialtime algorithms for deciding whether a given regular language is thin and whether a given regular code has decoding delay d, for given d, and for computing the minimum decoding delay of a given regular code.
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 15 (8 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.
Computing the edit distance of a regular language
 in Proc. of IEEE Information Theory Workshop on Coding and Complexity, Roturoa, New Zealand, Aug. 29
"... Abstract. The edit distance (or Levenshtein distance) between two words is the smallest number of substitutions, insertions, and deletions of symbols that can be used to transform one of the words into the other. In this paper we consider the problem of computing the edit distance of a regular langu ..."
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Cited by 10 (3 self)
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Abstract. The edit distance (or Levenshtein distance) between two words is the smallest number of substitutions, insertions, and deletions of symbols that can be used to transform one of the words into the other. In this paper we consider the problem of computing the edit distance of a regular language (also known as constraint system), that is, the set of words accepted by a given finite automaton. This quantity is the smallest edit distance between any pair of distinct words of the language. We show that the problem is of polynomial time complexity. We distinguish two cases depending on whether the given automaton is deterministic or nondeterministic. In the latter case the time complexity is higher. Incidentally, we also obtain an upper bound on the edit distance of a regular language in terms of the automaton accepting the language.
Coding Theory Codes as Formal Languages Methodologies Defining Code Properties Formal Methodologies
"... ..."
On properties of bondfree DNA languages
, 2005
"... The input data for DNA computing must be encoded into the form of single or double DNA strands. As complementary parts of single strands can bind together forming a doublestranded DNA sequence, one has to impose restrictions on these sets of DNA words (languages) to prevent them from interacting in ..."
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Cited by 14 (6 self)
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The input data for DNA computing must be encoded into the form of single or double DNA strands. As complementary parts of single strands can bind together forming a doublestranded DNA sequence, one has to impose restrictions on these sets of DNA words (languages) to prevent them from interacting in undesirable ways. We recall a list of known properties of DNA languages which are free of certain types of undesirable bonds. Then we introduce a general framework in which we can characterize each of these properties by a solution of a uniform formal language inequation. This characterization allows us among others to construct (i) a uniform algorithm deciding in polynomial time whether a given DNA language possesses any of the studied properties, and (ii) in many cases also an algorithm deciding whether a given DNA language is maximal with respect to the desired property.
Preventing undesirable bonds between DNA codewords
 Proceedings of the 10th International Meeting on DNA Computing, LNCS 3384
, 2005
"... Abstract. The input data for DNA computing must be encoded into the form of single or double DNA strands. As complementary parts of single strands can bind together forming a doublestranded DNA sequence, one has to impose restrictions on these sets of DNA words (=languages) to prevent them from int ..."
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Cited by 5 (3 self)
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Abstract. The input data for DNA computing must be encoded into the form of single or double DNA strands. As complementary parts of single strands can bind together forming a doublestranded DNA sequence, one has to impose restrictions on these sets of DNA words (=languages) to prevent them from interacting in undesirable ways. We recall a list of known properties of DNA languages which are free of certain types of undesirable bonds. Then we introduce a general framework in which we can characterize each of these properties by a solution of a uniform formal language inequation. This characterization allows us among others to construct (i) a uniform algorithm deciding in polynomial time whether a given DNA language possesses any of the studied properties, and (ii) in many cases also an algorithm deciding whether a given DNA language is maximal with respect to the desired property. 1
Hairpin structures in DNA words
 In The 11th International Meeting on DNA Computing: DNA 11, Preliminary Proceedings (2005
, 2006
"... Abstract. We formalize the notion of a DNA hairpin secondary structure, examining its mathematical properties. Two related secondary structures are also investigated, taking into the account imperfect bonds (bulges, mismatches) and multiple hairpins. We characterize maximal sets of hairpinforming D ..."
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Cited by 8 (4 self)
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Abstract. We formalize the notion of a DNA hairpin secondary structure, examining its mathematical properties. Two related secondary structures are also investigated, taking into the account imperfect bonds (bulges, mismatches) and multiple hairpins. We characterize maximal sets of hairpinforming DNA sequences, as well as hairpinfree ones. We study their algebraic properties and their computational complexity. Related polynomialtime algorithms deciding hairpinfreedom of regular sets are presented. Finally, effective methods for design of long hairpinfree DNA words are given. 1
ErrorDetecting Properties of Languages
 Theoretical Computer Science
, 2002
"... The language property of errordetection ensures that the communications medium cannot transform a word of the language to another word of the language. In this paper we provide some insights on the notion of errordetection from a language theoretic point of view. We de ne certain errordetecting p ..."
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Cited by 4 (3 self)
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The language property of errordetection ensures that the communications medium cannot transform a word of the language to another word of the language. In this paper we provide some insights on the notion of errordetection from a language theoretic point of view. We de ne certain errordetecting properties of languages and codes including the notion of errordetection with nite delay which is a natural extension of unique decodability with nite delay. We obtain results about the errordetecting capabilities of regular and other languages, and of known classes of codes. Moreover, we consider the problem of estimating the optimal redundancy of in nite languages with the property of detecting errors of the deletion type.
Results 1  10
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