Semantics and Complexity of SPARQL

TL;DR

This paper provides a formal analysis of SPARQL's graph pattern facility, establishing its semantics, normal forms, and computational complexity, specifically showing that pattern evaluation is PSPACE-complete.

Contribution

It offers a systematic formal study of SPARQL's semantics, complexity bounds, and conditions for semantic equivalence, advancing understanding of its theoretical foundations.

Findings

SPARQL pattern evaluation is PSPACE-complete.

Normal forms for SPARQL patterns exist.

Conditions identified when different semantics coincide.

Abstract

SPARQL is the W3C candidate recommendation query language for RDF. In this paper we address systematically the formal study of SPARQL, concentrating in its graph pattern facility. We consider for this study a fragment without literals and a simple version of filters which encompasses all the main issues yet is simple to formalize. We provide a compositional semantics, prove there are normal forms, prove complexity bounds, among others that the evaluation of SPARQL patterns is PSPACE-complete, compare our semantics to an alternative operational semantics, give simple and natural conditions when both semantics coincide and discuss optimizations procedures.