The Complexity of Datalog on Linear Orders

TL;DR

This paper investigates the computational complexity of datalog programs on linear orders, establishing EXPTIME-completeness for both finite and infinite cases, and extending results to Allen's interval algebra.

Contribution

It proves that datalog nonemptiness is EXPTIME-complete on all linear orders with at least two elements, including infinite orders, and applies this to Allen's interval algebra.

Findings

Datalog nonemptiness is EXPTIME-complete on all linear orders with ≥2 elements.

The result extends to infinite linear orders with constants.

Datalog nonemptiness on Allen's interval algebra is EXPTIME-complete.

Abstract

We study the program complexity of datalog on both finite and infinite linear orders. Our main result states that on all linear orders with at least two elements, the nonemptiness problem for datalog is EXPTIME-complete. While containment of the nonemptiness problem in EXPTIME is known for finite linear orders and actually for arbitrary finite structures, it is not obvious for infinite linear orders. It sharply contrasts the situation on other infinite structures; for example, the datalog nonemptiness problem on an infinite successor structure is undecidable. We extend our upper bound results to infinite linear orders with constants. As an application, we show that the datalog nonemptiness problem on Allen's interval algebra is EXPTIME-complete.