Conjunctive Regular Path Queries with String Variables

TL;DR

This paper introduces CXRPQ, a new class of graph queries with string variables that extend CRPQs, enabling expression of inter-path dependencies with manageable evaluation complexities in certain fragments.

Contribution

The paper defines CXRPQ, analyzes its expressive power, and identifies fragments with feasible evaluation complexities, bridging practical regex features with formal query frameworks.

Findings

CXRPQ can express inter-path dependencies not possible with CRPQs.

Certain fragments of CXRPQ have data complexity in NL.

Evaluation complexity varies from NL to NP, EXPSPACE depending on the fragment.

Abstract

We introduce the class CXRPQ of conjunctive xregex path queries, which are obtained from conjunctive regular path queries (CRPQs) by adding string variables (also called backreferences) as found in practical implementations of regular expressions. CXRPQs can be considered user-friendly, since they combine two concepts that are well-established in practice: pattern-based graph queries and regular expressions with backreferences. Due to the string variables, CXRPQs can express inter-path dependencies, which are not expressible by CRPQs. The evaluation complexity of CXRPQs, if not further restricted, is PSPACE-hard in data-complexity. We identify three natural fragments with more acceptable evaluation complexity: their data-complexity is in NL, while their combined complexity varies between EXPSPACE, PSPACE and NP. In terms of expressive power, we compare the CXRPQ-fragments with CRPQs and unions of CRPQs, and with extended conjunctive regular path queries (ECRPQs) and unions of ECRPQs.