Evaluating Datalog via Tree Automata and Cycluits

TL;DR

This paper demonstrates that certain classes of Datalog queries can be evaluated efficiently on structures with bounded treewidth by translating them into automata and cyclic circuits, enabling fixed-parameter tractability.

Contribution

It introduces a novel approach to evaluate clique-frontier-guarded Datalog with stratified negation using automata and cycluits, achieving fixed-parameter tractability.

Findings

Bilinear-time evaluation for CFG-Datalog on bounded treewidth structures.

Translation of queries into alternating two-way automata with cyclic provenance circuits.

Applicability to conjunctive queries, guarded negation fragment queries, and two-way regular path queries.

Abstract

We investigate parameterizations of both database instances and queries that make query evaluation fixed-parameter tractable in combined complexity. We show that clique-frontier-guarded Datalog with stratified negation (CFG-Datalog) enjoys bilinear-time evaluation on structures of bounded treewidth for programs of bounded rule size. Such programs capture in particular conjunctive queries with simplicial decompositions of bounded width, guarded negation fragment queries of bounded CQ-rank, or two-way regular path queries. Our result is shown by translating to alternating two-way automata, whose semantics is defined via cyclic provenance circuits (cycluits) that can be tractably evaluated.