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For an involution θ : Σ * → Σ * over a finite alphabet Σ we consider involution codes: θ-infix, θ-comma-free, θ-k-codes and θ-subword-k-codes. These codes arise from questions on DNA strand design. We investigate conditions under which both X and X + are same type of involution codes. General methods for generating such involution codes are given. The… (More)

This paper is a theoretical study of notions in combina-torics of words motivated by information being encoded as DNA strands in DNA computing. We generalize the classical notions of conjugacy and commutativity of words to incorporate the notion of an involution function, a formalization of the Watson-Crick complementarity of DNA single-strands. We define… (More)

One of the main research topics in DNA computing is associated with the design of information encoding single or double stranded DNA strands that are " suitable " for computation. Double stranded or partially double stranded DNA occurs as a result of binding between complementary DNA single strands (A is complementary to T and C is complementary to G). This… (More)

The study of hairpin-free words has been initiated in the context of DNA computing. DNA strands that, theoretically speaking, are finite strings over the alphabet {A, G, C, T} are used in DNA computing to encode information. Due to the fact that A is complementary to T and G to C, DNA single strands that are complementary can bind to each other or to… (More)

This paper provides an overview of existing approaches to encoding information on DNA strands for biocomputing, with a focus on the notion of Watson–Crick (WK) palindromes. We obtain a closed form for, as well as several properties of WK palindromes: The set of WK-palindromes is dense, context-free, but not regular, and is in general not closed under… (More)

In this paper we study a generalization of the classical notions of bordered and unbor-dered words, motivated by DNA computing. DNA strands can be viewed as finite strings over the alphabet {A, G, C, T }, and are used in DNA computing to encode information. Due to the fact that A is Watson-Crick complementary to T and G to C, DNA single strands that are… (More)

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… (More)

DNA strands that, mathematically speaking, are finite strings over the alphabet {A, G, C, T } are used in DNA computing to encode information. Due to the fact that A is Watson-Crick complementary to T and G to C, DNA single strands that are Watson-Crick complementary can bind to each other or to themselves in either intended or unintended ways. One of the… (More)