Monadic Datalog Containment on Trees Using the Descendant-Axis

TL;DR

This paper investigates the complexity of query containment for monadic datalog on trees with the descendant-axis, establishing that the problem is 2EXPTIME-hard, thus closing an open complexity gap.

Contribution

It proves that query containment with the descendant-axis in monadic datalog on trees is 2EXPTIME-hard, providing the exact complexity classification.

Findings

Query containment with descendant-axis is 2EXPTIME-hard.

Closes the open problem of exact complexity with descendant-axis.

Builds on previous results for child and firstchild axes.

Abstract

In their AMW14-paper, Frochaux, Grohe, and Schweikardt showed that the query containment problem for monadic datalog on finite unranked labeled trees is Exptime-complete when (a) considering unordered trees using the child-axis, and when (b) considering ordered trees using the axes firstchild, nextsibling, and child. Furthermore, when allowing to use also the descendant-axis, the query containment problem was shown to be solvable in 2-fold exponential time, but it remained open to determine the problems exact complexity in presence of the descendant-axis. The present paper closes this gap by showing that, in the presence of the descendant-axis, the problem is 2Exptime-hard.