Combined Tractability of Query Evaluation via Tree Automata and Cycluits (Extended Version)

TL;DR

This paper introduces a new Datalog fragment and a compilation approach to evaluate complex database queries efficiently on structures with bounded treewidth, while also analyzing the intractability of probabilistic query evaluation.

Contribution

It presents a novel Datalog fragment with linear-time evaluation on bounded treewidth structures and a compilation method using cyclic provenance circuits for fixed-parameter tractability.

Findings

Efficient evaluation of conjunctive and guarded negation queries on bounded treewidth.

Compilation to cyclic provenance circuits enables tractable query evaluation.

Probabilistic query evaluation remains intractable despite new methods.

Abstract

We investigate parameterizations of both database instances and queries that make query evaluation fixed-parameter tractable in combined complexity. We introduce a new Datalog fragment with stratified negation, intensional-clique-guarded Datalog (ICG-Datalog), with linear-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 proceeds via compilation to alternating two-way automata, whose semantics is defined via cyclic provenance circuits (cycluits) that can be tractably evaluated. Last, we prove that probabilistic query evaluation remains intractable in combined complexity under this parameterization.