A connection between String Covers and Cover Deterministic Finite Tree Automata Minimization

TL;DR

This paper extends the concept of string covers to trees, introduces deterministic tree automata, and explores the complexity and minimization of cover problems, with applications to data compression.

Contribution

It generalizes string cover models to trees, introduces deterministic tree automata, and analyzes the complexity and minimization of cover problems in this new context.

Findings

Bounds for the Cover Minimization Problem

Complexity analysis in sequential and parallel settings

Optimal solution for the Shortest Common Cover Problem

Abstract

Data compression plays a crucial part in the cloud based systems of today. One the fundaments of compression is quasi-periodicity, for which there are several models. We build upon the most popular quasi-periodicity model for strings, i.e., covers, generalizing it to trees. We introduce a new type of cover automata, which we call \textbf{D}eterministic \textbf{T}ree \textbf{A}utomata. Then, we formulate a cover problem on these DTA and study its complexity, in both sequential and parallel settings. We obtain bounds for the Cover Minimization Problem. Along the way, we uncover an interesting application, the Shortest Common Cover Problem, for which we give an optimal solution.