Wim Martens ; Matthias Niewerth ; Tina Popp - A Trichotomy for Regular Trail Queries

lmcs:8604 - Logical Methods in Computer Science, December 7, 2023, Volume 19, Issue 4 - https://doi.org/10.46298/lmcs-19(4:20)2023
A Trichotomy for Regular Trail QueriesPreprint

Authors: Wim Martens ; Matthias Niewerth ; Tina Popp

    Regular path queries (RPQs) are an essential component of graph query languages. Such queries consider a regular expression r and a directed edge-labeled graph G and search for paths in G for which the sequence of labels is in the language of r. In order to avoid having to consider infinitely many paths, some database engines restrict such paths to be trails, that is, they only consider paths without repeated edges. In this paper we consider the evaluation problem for RPQs under trail semantics, in the case where the expression is fixed. We show that, in this setting, there exists a trichotomy. More precisely, the complexity of RPQ evaluation divides the regular languages into the finite languages, the class Ttract (for which the problem is tractable), and the rest. Interestingly, the tractable class in the trichotomy is larger than for the trichotomy for simple paths, discovered by Bagan, Bonifati, and Groz [JCSS 2020]. In addition to this trichotomy result, we also study characterizations of the tractable class, its expressivity, the recognition problem, closure properties, and show how the decision problem can be extended to the enumeration problem, which is relevant to practice.

    Volume: Volume 19, Issue 4
    Published on: December 7, 2023
    Accepted on: August 23, 2023
    Submitted on: October 26, 2021
    Keywords: Computer Science - Formal Languages and Automata Theory,Computer Science - Databases,Computer Science - Logic in Computer Science

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