Coding Properties of DNA Languages

Hussini, Salah; Kari, Lila; Konstantinidis, Stavros

doi:10.1007/3-540-48017-x_6

Cited by 28 publications

(36 citation statements)

References 7 publications

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“…In [9], the authors introduce the concept of a strictly τ -free code K, which is a generalization of the notion of comma-free code [12], and show that the language K + must be strictly τ -free as well. Here we shall assume that K is of fixed length k. In this formalization the tube language L is equal to K + .…”

Section: P1[k]mentioning

confidence: 99%

Bond-Free Languages: Formalizations, Maximality and Construction Methods

2005

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Abstract. The problem of negative design of DNA languages is addressed, that is, properties and construction methods of large sets of words that prevent undesired bonds when used in DNA computations. We recall a few existing formalizations of the problem and then define the property of sim-bond-freedom, where sim is a similarity relation between words. We show that this property is decidable for context-free languages and polynomial-time decidable for regular languages. The maximality of this property also turns out to be decidable for regular languages and polynomial-time decidable for an important case of the Hamming similarity. Then we consider various construction methods for Hamming bond-free languages, including the recently introduced method of templates, and obtain a complete structural characterization of all maximal Hamming bond-free languages. This result is applicable to the θ-k-code property introduced by Jonoska and Mahalingam.

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Section: P1[k]mentioning

confidence: 99%

Bond-Free Languages: Formalizations, Maximality and Construction Methods

2005

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“…1 (a), and intermolecular, (b) and (c). The following properties of a DNA language L ⊆ Σ + preventing such a hybridization have been defined in [4,8,10].…”

Section: Undesirable Bonds In Dna Languagesmentioning

confidence: 99%

“…In [4] the decidability of the properties (D) and (F) for regular sets of words was shown. In [3] the decidability of (M) in quadratic time is proven.…”

Section: Output: Y/n Depending On Whether L(a) Satisfies Pmentioning

confidence: 99%

“…On the other hand, it is known [4] that for some bond-free properties, e.g. (B) and (F), there is no such algorithm in the case of context-free DNA languages.…”

Section: Output: Y/n Depending On Whether L(a) Satisfies Any Of the Pmentioning

confidence: 99%

“…See e.g. [1,3,4,5,6,8,10,13] for studies of properties of such sets (called also DNA languages) and methods of their construction.…”

Section: Introductionmentioning

confidence: 99%

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Preventing Undesirable Bonds Between DNA Codewords

2005

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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 double-stranded 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.

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Involution Solid and Join Codes

Jonoska

Kari

Mahalingam

2006

Developments in Language Theory

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In this paper we study a generalization of the classical notions of solid codes and comma-free codes: involution solid codes (θ-solid) and involution join codes (θ-join). These notions are motivated by DNA strand design where Watson-Crick complementarity can be formalized as an antimorphic involution. We investigate closure properties of these codes, as well as necessary conditions for θ-solid codes to be maximal. We show how the concept of θ-join can be utilized such that codes that are not themselves θ-comma free can be split into a union of subcodes that are θ-comma free.

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Coding Properties of DNA Languages

Cited by 28 publications

References 7 publications

Bond-Free Languages: Formalizations, Maximality and Construction Methods

Bond-Free Languages: Formalizations, Maximality and Construction Methods

Preventing Undesirable Bonds Between DNA Codewords

Involution Solid and Join Codes

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