Superposition Based on Watson–Crick-Like Complementarity

Further remarks on DNA overlap assembly

“…In other words, the iterated overlap assembly is a special case of the iterated superposition. Therefore, the (positive) closure results for the iterated superposition, obtained in [22,31], also hold for the iterated overlap assembly. Indeed, the same results were independently obtained in [1], in its study of closure properties of iterated overlap assembly:…”

“…The superposition operation is a binary operation proposed by Bottoni, Labella, Manca, and Mitrana in [22] to model the action of the DNA Polymerase enzyme. The result of the superposition operation between words x, y ∈ Σ + , denoted by x y, consists of the set of all words z ∈ Σ + obtained by any of the four following cases (¯denotes the morphic complement, that is,¯is a morphism such that u = u for all words u):…”

“…For more on the superposition operation between two words (languages), the reader is referred to [22,31].…”

“…The result that the family of context-free languages is not closed under iterated overlap assembly (resp., iterated superposition) was proven in [1] (resp., [22]). The following statement strengthens that result.…”

“…In this paper, following Section 2 comprising definitions, notations and basic properties, in Section 3 we correlate the overlap assembly operation with the superposition operation introduced in [22] and determine additional closure properties of some language classes under iterated overlap assembly. A string w is terminal with respect to a language L if w ∈ L and the result of the overlap assembly between w and L equals {w}; the terminal set T (L) contains all words that are terminal with respect to L. In Section 4 we investigate the closure properties of terminal sets of complete languages (languages closed under overlap assembly).…”