# On the ambiguity of insertion systems

TL;DR: This paper defines six levels of ambiguity for insertion systems based on the components used in the derivation such as axiom, contexts and strings and shows that there are inherently i-ambiguous insertion languages which are j-unambiguous for the combinations (i, j).

Abstract: Gene insertion and deletion are the operations that occur commonly in DNA processing and RNA editing. Based on these evolutionary transformations, a computing model has been formulated in formal language theory known as insertion-deletion systems. In this paper, we study about the ambiguity issues of insertion systems. First, we define six levels of ambiguity for insertion systems based on the components used in the derivation such as axiom, contexts and strings. Next, we show that there are inherently i-ambiguous insertion languages which are j-unambiguous for the combinations (i, j) ∈ {(5,0), (5,4), (4,3), (4,2), (3,1),(2,1), (1,0), (0,1)}. Finally, we prove an important result that the ambiguity problem of insertion systems is undecidable.

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### "On the ambiguity of insertion syste..." refers background in this paper

...The area includes DNA computing [6],membrane computing [9] and evolutionary computing [1] among other topics....

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...The developments have taken place in DNA computing inspired the definition and study of new theoretical models in formal language theory, such as sticker systems, splicing systems, Watson-Crick automata and insertion-deletion systems [3, 6]....

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131 citations