Resilience for Regular Path Queries: Towards a Complexity Classification

TL;DR

This paper investigates the computational complexity of resilience in Regular Path Queries over graph databases, identifying classes of languages where resilience computation is tractable or hard, advancing understanding of query robustness.

Contribution

It characterizes the complexity of computing resilience for RPQs based on the regular language class, providing a dichotomy between tractable and hard cases.

Findings

Tractability for local languages in resilience computation.

Hardness results for non-local languages, including star-free and languages with neutral letters.

Identification of specific language classes with computational complexity implications.

Abstract

The resilience problem for a query and an input set or bag database is to compute the minimum number of facts to remove from the database to make the query false. In this paper, we study how to compute the resilience of Regular Path Queries (RPQs) over graph databases. Our goal is to characterize the regular languages L for which it is tractable to compute the resilience of the existentially-quantified RPQ built from L. We show that computing the resilience in this sense is tractable (even in combined complexity) for all RPQs defined from so-called local languages. By contrast, we show hardness in data complexity for RPQs defined from the following language classes (after reducing the languages to eliminate redundant words): all finite languages featuring a word containing a repeated letter, and all languages featuring a specific kind of counterexample to being local (which we call four-legged languages). The latter include in particular all languages that are not star-free. Our results also imply hardness for all non-local languages with a so-called neutral letter. We last show tractability for some classes of non-local languages, namely the so-called bipartite chain languages and one-dangling languages, and highlight some remaining obstacles towards a full dichotomy.