Tractable Circuits in Database Theory

TL;DR

This paper explores how tractable circuit classes from knowledge compilation can be applied to database query evaluation, provenance, and enumeration tasks, especially for MSO queries and CQs/UCQs.

Contribution

It provides a comprehensive review of tractable circuits in database theory and demonstrates their applications to various query evaluation and provenance tasks.

Findings

Tractable circuits enable efficient Boolean provenance computation.

They facilitate probabilistic query evaluation on trees.

Circuit representations improve enumeration of query answers.

Abstract

This work reviews how database theory uses tractable circuit classes from knowledge compilation. We present relevant query evaluation tasks, and notions of tractable circuits. We then show how these tractable circuits can be used to address database tasks. We first focus on Boolean provenance and its applications for aggregation tasks, in particular probabilistic query evaluation. We study these for Monadic Second Order (MSO) queries on trees, and for safe Conjunctive Queries (CQs) and Union of Conjunctive Queries (UCQs). We also study circuit representations of query answers, and their applications to enumeration tasks: both in the Boolean setting (for MSO) and the multivalued setting (for CQs and UCQs).