Conjunctive Regular Path Queries under Injective Semantics

We introduce injective semantics for Conjunctive Regular Path Queries (CRPQs), and study their fundamental properties. We identify two such semantics: atom-injective and query-injective semantics, both defined in terms of injective homomorphisms. These semantics are natural generalizations of the well-studied class of RPQs under simple-path semantics to the class of CRPQs. We study their evaluation and containment problems, providing useful characterizations for them, and we pinpoint the complexities of these problems. Perhaps surprisingly, we show that containment for CRPQs becomes undecidable for atom-injective semantics, and PSPACE-complete for query-injective semantics, in contrast to the known EXPSPACE-completeness result for the standard semantics. The techniques used differ significantly from the ones known for the standard semantics, and new tools tailored to injective semantics are needed. We complete the picture of complexity by investigating, for each semantics, the containment problem for the main subclasses of CRPQs, namely Conjunctive Queries and CRPQs with finite languages.Comment: Accepted in the Proceedings of the 42nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems (PODS '23

Eliminating Recursion from Monadic Datalog Programs on Trees

We study the problem of eliminating recursion from monadic datalog programs on trees with an infinite set of labels. We show that the boundedness problem, i.e., determining whether a datalog program is equivalent to some nonrecursive one is undecidable but the decidability is regained if the descendant relation is disallowed. Under similar restrictions we obtain decidability of the problem of equivalence to a given nonrecursive program. We investigate the connection between these two problems in more detail

The Dichotomy of Evaluating Homomorphism-Closed Queries on Probabilistic Graphs

We study the problem of probabilistic query evaluation on probabilistic graphs, namely, tuple-independent probabilistic databases on signatures of arity two. Our focus is the class of queries that is closed under homomorphisms, or equivalently, the infinite unions of conjunctive queries. Our main result states that all unbounded queries from this class are #P-hard for probabilistic query evaluation. As bounded queries from this class are equivalent to a union of conjunctive queries, they are already classified by the dichotomy of Dalvi and Suciu (2012). Hence, our result and theirs imply a complete data complexity dichotomy, between polynomial time and #P-hardness, for evaluating infinite unions of conjunctive queries over probabilistic graphs. This dichotomy covers in particular all fragments of infinite unions of conjunctive queries such as negation-free (disjunctive) Datalog, regular path queries, and a large class of ontology-mediated queries on arity-two signatures. Our result is shown by reducing from counting the valuations of positive partitioned 2-DNF formulae for some queries, or from the source-to-target reliability problem in an undirected graph for other queries, depending on properties of minimal models. The presented dichotomy result applies to even a special case of probabilistic query evaluation called generalized model counting, where fact probabilities must be 0, 0.5, or 1.Comment: 30 pages. Journal version of the ICDT'20 paper https://drops.dagstuhl.de/opus/volltexte/2020/11939/. Submitted to LMCS. The previous version (version 2) was the same as the ICDT'20 paper with some minor formatting tweaks and 7 extra pages of technical appendi

The fine classification of conjunctive queries and parameterized logarithmic space

We perform a fundamental investigation of the complexity of conjunctive query evaluation from the perspective of parameterized complexity. We classify sets of boolean conjunctive queries according to the complexity of this problem. Previous work showed that a set of conjunctive queries is fixed-parameter tractable precisely when the set is equivalent to a set of queries having bounded treewidth. We present a fine classification of query sets up to parameterized logarithmic space reduction. We show that, in the bounded treewidth regime, there are three complexity degrees and that the properties that determine the degree of a query set are bounded pathwidth and bounded tree depth. We also engage in a study of the two higher degrees via logarithmic space machine characterizations and complete problems. Our work yields a significantly richer perspective on the complexity of conjunctive queries and, at the same time, suggests new avenues of research in parameterized complexity