Site-Directed Insertion: Decision Problems, Maximality and Minimality

Abstract

Site-directed insertion is an overlapping insertion operation that can be viewed as analogous to the overlap assembly or chop operations that concatenate strings by overlapping a suffix and a prefix of the argument strings. We consider decision problems and language equations involving site-directed insertion. By relying on the tools provided by semantic shuffle on trajectories we show that one variable equations involving site-directed insertion and regular constants can be solved. We consider also maximal and minimal variants of the site-directed insertion operation.

Site-directed insertion: Language equations and decision problems

“…An outfix of a string consists of a prefix and suffix of the string that do not overlap. Site-directed insertion (SDI) of a string y into a string x involves matching an outfix of y $ A preliminary version of this paper [4] Email addresses: da-jung.cho@lsv.fr,dajung.cho@lri.fr (Da-Jung Cho), emmous@yonsei.ac.kr (Yo-Sub Han), ksalomaa@cs.queensu.ca (Kai Salomaa), tsmith@cs.queensu.ca (Taylor J. Smith) with a substring of x and inserting the "middle part" of y not belonging to the outfix into x. Site-directed insertion has earlier been considered under the name outfix-guided insertion [3]. The operation is an overlapping variant of the insertion operation in the same sense as the overlap assembly, a.k.a.…”