# Subsumption of Weakly Well-Designed SPARQL Patterns is Undecidable

## TL;DR

This paper proves that determining whether one weakly well-designed SPARQL pattern subsumes another is an undecidable problem, highlighting a significant computational complexity difference from well-designed patterns.

## Contribution

It establishes the undecidability of subsumption for weakly well-designed SPARQL patterns, contrasting with known decidability results for well-designed patterns.

## Key findings

- Subsumption is undecidable for weakly well-designed patterns.
- Contrasts with decidability of equivalence and containment.
- Highlights computational complexity challenges in SPARQL analysis.

## Abstract

Weakly well-designed SPARQL patterns is a recent generalisation of well-designed patterns, which preserve good computational properties but also capture almost all patterns that appear in practice. Subsumption is one of static analysis problems for SPARQL, along with equivalence and containment. In this paper we show that subsumption is undecidable for weakly well-designed patterns, which is in stark contrast to well-designed patterns, and to equivalence and containment.