ON THE AMBIGUITY OF INSERTION SYSTEMS
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) is an element of {(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.
insertion systems undecidability inherently ambiguous languages unambiguous system