Site-Directed Insertion: Decision Problems, Maximality and Minimality

TL;DR

This paper investigates decision problems and equations involving site-directed insertion, an overlapping string operation, and explores maximal and minimal variants, providing solutions using semantic shuffle techniques.

Contribution

It introduces decision problem analysis and solutions for site-directed insertion equations, including maximal and minimal variants, using semantic shuffle on trajectories.

Findings

One variable equations with site-directed insertion and regular constants can be solved.

Maximal and minimal variants of site-directed insertion are characterized.

Semantic shuffle on trajectories is effective for solving related decision problems.

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.