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On Deciding the Data Complexity of Answering Linear Monadic Datalog Queries with LTL Operators

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Bibliographic Details
Title: On Deciding the Data Complexity of Answering Linear Monadic Datalog Queries with LTL Operators
Authors: Artale, Alessandro, Gnatenko, Anton, Ryzhikov, Vladislav, Zakharyaschev, Michael
Contributors: Alessandro Artale and Anton Gnatenko and Vladislav Ryzhikov and Michael Zakharyaschev
Publisher Information: Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2025.
Publication Year: 2025
Subject Terms: data complexity, ddc:004, Linear monadic datalog, linear temporal logic
Description: Our concern is the data complexity of answering linear monadic datalog queries whose atoms in the rule bodies can be prefixed by operators of linear temporal logic LTL. We first observe that, for data complexity, answering any connected query with operators ○/○- (at the next/previous moment) is either in AC⁰, or in ACC⁰\AC⁰, or NC¹-complete, or L-hard and in NL. Then we show that the problem of deciding L-hardness of answering such queries is PSpace-complete, while checking membership in the classes AC⁰ and ACC⁰ as well as NC¹-completeness can be done in ExpSpace. Finally, we prove that membership in AC⁰ or in ACC⁰, NC¹-completeness, and L-hardness are undecidable for queries with operators ◇/◇- (sometime in the future/past) provided that NC¹ ≠ NL and L ≠ NL.
Document Type: Conference object
File Description: application/pdf
Language: English
DOI: 10.4230/lipics.icdt.2025.31
Access URL: https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.31
Rights: CC BY
Accession Number: edsair.od......1814..c7a90792dfef92c2276bb382dd2f8fdb
Database: OpenAIRE
Description
Abstract:Our concern is the data complexity of answering linear monadic datalog queries whose atoms in the rule bodies can be prefixed by operators of linear temporal logic LTL. We first observe that, for data complexity, answering any connected query with operators ○/○- (at the next/previous moment) is either in AC⁰, or in ACC⁰\AC⁰, or NC¹-complete, or L-hard and in NL. Then we show that the problem of deciding L-hardness of answering such queries is PSpace-complete, while checking membership in the classes AC⁰ and ACC⁰ as well as NC¹-completeness can be done in ExpSpace. Finally, we prove that membership in AC⁰ or in ACC⁰, NC¹-completeness, and L-hardness are undecidable for queries with operators ◇/◇- (sometime in the future/past) provided that NC¹ ≠ NL and L ≠ NL.
DOI:10.4230/lipics.icdt.2025.31