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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 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(More)
The computation language of a DNA-based system consists of all the words (DNA strands) that can appear in any computation step of the system. In this work we deene 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(More)
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 hairpin-forming DNA sequences, as well as hairpin-free ones. We study their algebraic(More)
The paper examines the concept of hairpin-free words motivated from the biocomputing and bioinformatics fields. Hairpin (free) DNA structures have numerous applications to DNA computing and molecular genetics in general. A word is called hairpin-free if it cannot be written in the form xvyθ(v)z, with certain additional conditions, for an involution θ (a(More)
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(More)
—We investigate the problem of designing pairs () of words with the property that, if each word of a coded message is prefixed by and suffixed by , the resulting set of coded messages is error detecting with finite delay. We consider (combinatorial) channels permitting any combination of the substitution, insertion, and deletion (SID) error types, and(More)
An essential step of any DNA computation is encoding the input data on single or double DNA strands. Due to the biochemical properties of DNA, complementary single strands can bind to one another forming double-stranded DNA. Consequently, data-encoding DNA strands can sometimes interact in undesirable ways when used in computations. It is crucial thus to(More)
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(More)
Xρóνια πoλλ´α κ´υριε Γ ιo´υργκενσεν. E ´ υχoµαι να τ α εκατ oστ´ησετ ε. Abstract: When the words of a language are communicated via a noisy channel, the language property of error-detection ensures that no word of the language can be transformed to another word of the language. On the other hand, the property of error-correction ensures that the channel(More)