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Data compression plays a crucial part in the cloud based systems of today.One the fundaments of compression is quasi-periodicity, for which there areseveral models. We build upon the most popular quasi-periodicity model forstrings, 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 acover problem on these DTA and study its complexity, in both sequential andparallel settings. We obtain bounds for the Cover Minimization Problem. Alongthe way, we uncover an interesting application, the Shortest Common CoverProblem, for which we give an optimal solution.

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