The resilience problem for a query and an input set or bag database is to compute the minimum number of facts to remove from the database to make the query false. In this paper, we study how to compute the resilience of Regular Path Queries (RPQs) over graph databases. Our goal is to characterize the regular languages L for which it is tractable to compute the resilience of the existentially-quantified RPQ built from L . We show that computing the resilience in this sense is tractable (even in combined complexity) for all RPQs defined from so-called local languages . By contrast, we show hardness in data complexity for RPQs defined from the following language classes (after reducing the languages to eliminate redundant words): all finite languages featuring a word containing a repeated letter, and all languages featuring a specific kind of counterexample to being local (which we call four-legged languages). The latter include in particular all languages that are not star-free . Our results also imply hardness for all non-local languages with a so-called neutral letter . We last highlight some remaining obstacles towards a full dichotomy.

We study the problem of enumerating the satisfying assignments for circuit classes from knowledge compilation, where assignments are ranked in a specific order. In particular, we show how this problem can be used to efficiently perform ranked enumeration of the answers to MSO queries over trees, with the order being given by a ranking function satisfying a subset-monotonicity property. Assuming that the number of variables is constant, we show that we can enumerate the satisfying assignments in ranked order for so-called multivalued circuits that are smooth, decomposable, and in negation normal form (smooth multivalued DNNF). There is no preprocessing and the enumeration delay is linear in the size of the circuit times the number of values, plus a logarithmic term in the number of assignments produced so far. If we further assume that the circuit is deterministic (smooth multivalued d-DNNF), we can achieve linear-time preprocessing in the circuit, and the delay only features the logarithmic term.

Shapley values, originating in game theory and increasingly prominent in explainable AI, have been proposed to assess the contribution of facts in query answering over databases, along with other similar power indices such as Banzhaf values. In this work we adapt these Shapley-like scores to probabilistic settings, the objective being to compute their expected value. We show that the computations of expected Shapley values and of the expected values of Boolean functions are interreducible in polynomial time, thus obtaining the same tractability landscape. We investigate the specific tractable case where Boolean functions are represented as deterministic decomposable circuits, designing a polynomial-time algorithm for this setting. We present applications to probabilistic databases through database provenance, and an effective implementation of this algorithm within the ProvSQL system, which experimentally validates its feasibility over a standard benchmark.

Explaining query results is an essential tool for enhancing the transparency and quality of data processing, and has been extensively studied in recent years. In particular, Data Provenance -- the tracking of transformations that data undergoes in query evaluation -- has been shown to be a key component of explanations. A hurdle that remains is that data provenance itself is often too large and complex to be presented in its entirety. To that end, we propose to leverage novel advancements on quantifying and computing the contributions of individual input tuples to query answers, based on the game-theoretic notion of the Shapley value. Our proposed prototype solution, called ShapGraph, combines the global view of explanations through provenance graphs with a local quantification of contributions through Shapley values. The graphical interface allows users to switch between and combine these two views to obtain a deeper understanding of the most influential parts of the database and how they interact to yield query answers.

The Shapley value is a game-theoretic notion for wealth distribution that is nowadays extensively used to explain complex data-intensive computation, for instance, in network analysis or machine learning. Recent theoretical works show that query evaluation over relational databases fits well in this explanation paradigm. Yet, these works fall short of providing practical solutions to the computational challenge inherent to the Shapley computation. We present in this paper two practically effective solutions for computing Shapley values in query answering. We start by establishing a tight theoretical connection to the extensively studied problem of query evaluation over probabilistic databases, which allows us to obtain a polynomial-time algorithm for the class of queries for which probability computation is tractable. We then propose a first practical solution for computing Shapley values that adopts tools from probabilistic query evaluation. In particular, we capture the dependence of query answers on input database facts using Boolean expressions (data provenance), and then transform it, via Knowledge Compilation, into a particular circuit form for which we devise an algorithm for computing the Shapley values. Our second practical solution is a faster yet inexact approach that transforms the provenance to a Conjunctive Normal Form and uses a heuristic to compute the Shapley values. Our experiments on TPC-H and IMDB demonstrate the practical effectiveness of our solutions.

We study the complexity of various fundamental counting problems that arise in the context of incomplete databases, i.e., relational databases that can contain unknown values in the form of labeled nulls. Specifically, we assume that the domains of these unknown values are finite and, for a Boolean query q, we consider the following two problems: given as input an incomplete database D, (a) return the number of completions of D that satisfy q; or (b) return or the number of valuations of the nulls of D yielding a completion that satisfies q. We obtain dichotomies between #P-hardness and polynomial-time computability for these problems when q is a self-join-free conjunctive query, and study the impact on the complexity of the following two restrictions: (1) every null occurs at most once in D (what is called Codd tables); and (2) the domain of each null is the same. Roughly speaking, we show that counting completions is much harder than counting valuations (for instance, while the latter is always in #P, we prove that the former is not in #P under some widely believed theoretical complexity assumption). Moreover, we find that both (1) and (2) reduce the complexity of our problems. We also study the approximability of these problems and show that, while counting valuations always has a fully polynomial randomized approximation scheme, in most cases counting completions does not. Finally, we consider more expressive query languages and situate our problems with respect to known complexity classes.

We consider the problem of exact probabilistic inference for Union of Conjunctive Queries (UCQs) on tuple-independent databases. For this problem, two approaches currently coexist. In the extensional method, query evaluation is performed by exploiting the structure of the query, and relies heavily on the use of the inclusion--exclusion principle. In the intensional method, one first builds a representation of the lineage of the query in a tractable formalism of knowledge compilation. The chosen formalism should then ensure that the probability can be efficiently computed using simple disjointness and independence assumptions, without the need of performing inclusion--exclusion. The extensional approach has long been thought to be strictly more powerful than the intensional approach, the reason being that for some queries, the use of inclusion--exclusion seemed unavoidable. In this paper we introduce a new technique to construct lineage representations as deterministic decomposable circuits in polynomial time. We prove that this technique applies to a class of UCQs that had been conjectured to separate the complexity of the two approaches. In essence, we show that relying on the inclusion--exclusion formula can be avoided by using negation. This result brings back hope to prove that the intensional approach can handle all tractable UCQs.

33 pages, no figures, 40 references. This is the full version with proofs of the corresponding ICDT'18 publication, and it integrates all reviewer feedback. Except for the additional appendices, and except for formatting differences and inessential changes, the contents are the same as in the conference version

Several query evaluation tasks can be done via knowledge compilation: the query result is compiled as a lineage circuit from which the answer can be determined. For such tasks, it is important to leverage some width parameters of the circuit, such as bounded treewidth or pathwidth, to convert the circuit to structured classes, e.g., deterministic structured NNFs (d-SDNNFs) or OBDDs. In this work, we show how to connect the width of circuits to the size of their structured representation, through upper and lower bounds. For the upper bound, we show how bounded-treewidth circuits can be converted to a d-SDNNF, in time linear in the circuit size. Our bound, unlike existing results, is constructive and only singly exponential in the treewidth. We show a related lower bound on monotone DNF or CNF formulas, assuming a constant bound on the arity (size of clauses) and degree (number of occurrences of each variable). Specifically, any d-SDNNF (resp., SDNNF) for such a DNF (resp., CNF) must be of exponential size in its treewidth; and the same holds for pathwidth when compiling to OBDDs. Our lower bounds, in contrast with most previous work, apply to any formula of this class, not just a well-chosen family. Hence, for our language of DNF and CNF, pathwidth and treewidth respectively characterize the efficiency of compiling to OBDDs and (d-)SDNNFs, that is, compilation is singly exponential in the width parameter. We conclude by applying our lower bound results to the task of query evaluation.

Query evaluation over probabilistic databases is known to be intractable in many cases, even in data complexity, i.e., when the query is fixed. Although some restrictions of the queries and instances[4] have been proposed to lower the complexity, these known tractable cases usually do not apply to combined complexity, i.e., when the query is not fixed. This leaves open the question of which query and instance languages ensure the tractability of probabilistic query evaluation in combined complexity.