Overall Objectives
Research Program
Application Domains
New Software and Platforms
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
Bibliography
 PDF e-Pub

## Section: New Results

### Foundations of data management

We obtained a number of results on the foundations of data management, i.e., in database theory.

We worked on knowledge bases. In our work a knowledge base consists of an incomplete database together with a set of existential rules. We investigated the problem of query answering: computing the answers that are logically entailed from the knowledge base. This brings to light the fundamental chase tool, and its different variants that have been proposed in the literature. We studied the problem of chase termination, which has applications beyond query answering, and studied its complexity for restricted but useful classes of existential rules [27].

We worked on data integration. In our scenario a user can access data sitting in multiple sources by means of queries over a global schema, related to the sources via mappings. Data sources often contain sensitive information, and thus an analysis is needed to verify that a schema satisfies a privacy policy, given as a set of queries whose answers should not be accessible to users. We show that source constraints can have a dramatic impact on disclosure analysis [22]. Another work related to data integration is [16], where we connect the problem of answering queries under limited accesses (e.g., using Web forms) to two foundational issues: containment of Monadic datalog (MDL) programs, and containment problems involving regular tree languages. In particular, we establish a 2EXPTIME lower bound on the problem of containment of a MDL program into a conjunctive query, resolving an open problem from the early 1990s.

We also considered some other foundational topics, further from core database topics. In [18], we establish bounds on the height of maximal finite towers (a tower is a sequence of words alternating between two languages in such a way that every word is a subsequence of the following word) between two regular languages. In [17], we present an online $O\left(\sigma |y|\right)$-time algorithm for finding approximate occurrences of a word $x$ within a word $y$, where $\sigma$ is the alphabet size.

Note that two other works in this theme will be described in the 2020 activity report, as they are published in 2020 conferences [25], [26].