Overall Objectives
Research Program
Application Domains
New Software and Platforms
Partnerships and Cooperations
Bibliography
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## Section: Research Program

### Scientific Foundations

We now detail some of the scientific foundations of our research on complex data management. This is the occasion to review connections between data management, especially on complex data as is the focus of Valda, with related research areas.

#### Complexity & Logic.

Data management has been connected to logic since the advent of the relational model as main representation system for real-world data, and of first-order logic as the logical core of database querying languages [43]. Since these early developments, logic has also been successfully used to capture a large variety of query modes, such as data aggregation [76], recursive queries (Datalog), or querying of XML databases [55]. Logical formalisms facilitate reasoning about the expressiveness of a query language or about its complexity.

The main problem of interest in data management is that of query evaluation, i.e., computing the results of a query over a database. The complexity of this problem has far-reaching consequences. For example, it is because first-order logic is in the ${\text{AC}}_{0}$ complexity class that evaluation of SQL queries can be parallelized efficiently. It is usual [89] in data management to distinguish data complexity, where the query is considered to be fixed, from combined complexity, where both the query and the data are considered to be part of the input. Thus, though conjunctive queries, corresponding to a simple SELECT-FROM-WHERE fragment of SQL, have PTIME data complexity, they are NP-hard in combined complexity. Making this distinction is important, because data is often far larger (up to the order of terabytes) than queries (rarely more than a few hundred bytes). Beyond simple query evaluation, a central question in data management remains that of complexity; tools from algorithm analysis, and complexity theory can be used to pinpoint the tractability frontier of data management tasks.

#### Automata Theory.

Automata theory and formal languages arise as important components of the study of many data management tasks: in temporal databases [42], queries, expressed in temporal logics, can often by compiled to automata; in graph databases [51], queries are naturally given as automata; typical query and schema languages for XML databases such as XPath and XML Schema can be compiled to tree automata [81], or for more complex languages to data tree automata[4]. Another reason of the importance of automata theory, and tree automata in particular, comes from Courcelle's results [59] that show that very expressive queries (from the language of monadic second-order language) can be evaluated as tree automata over tree decompositions of the original databases, yielding linear-time algorithms (in data complexity) for a wide variety of applications.

#### Verification.

Complex data management also has connections to verification and static analysis. Besides query evaluation, a central problem in data management is that of deciding whether two queries are equivalent [43]. This is critical for query optimization, in order to determine if the rewriting of a query, maybe cheaper to evaluate, will return the same result as the original query. Equivalence can easily be seen to be an instance of the problem of (non-)satisfiability: $q\equiv {q}^{\text{'}}$ if and only if $\left(q\wedge ¬{q}^{\text{'}}\right)\vee \left(¬q\wedge {q}^{\text{'}}\right)$ is not satisfiable. In other words, some aspects of query optimization are static analysis issues. Verification is also a critical part of any database application where it is important to ensure that some property will never (or always) arise [57].

#### Probability & Provenance.

To deal with the uncertainty attached to data, proper models need to be used (such as attaching provenance information to data items and viewing the whole database as being probabilistic) and practical methods and systems need to be developed to both reliably estimate the uncertainty in data items and properly manage provenance and uncertainty information throughout a long, complex system.

The simplest model of data uncertainty is the NULLs of SQL databases, also called Codd tables [43]. This representation system is too basic for any complex task, and has the major inconvenient of not being closed under even simple queries or updates. A solution to this has been proposed in the form of conditional tables [73] where every tuple is annotated with a Boolean formula over independent Boolean random events. This model has been recognized as foundational and extended in two different directions: to more expressive models of provenance than what Boolean functions capture, through a semiring formalism [69], and to a probabilistic formalism by assigning independent probabilities to the Boolean events [70]. These two extensions form the basis of modern provenance and probability management, subsuming in a large way previous works [58], [52]. Research in the past ten years has focused on a better understanding of the tractability of query answering with provenance and probabilistic annotations, in a variety of specializations of this framework [87] [75], [48].

#### Machine Learning.

Statistical machine learning, and its applications to data mining and data analytics, is a major foundation of data management research. A large variety of research areas in complex data management, such as wrapper induction [83], crowdsourcing [50], focused crawling [68], or automatic database tuning [53] critically rely on machine learning techniques, such as classification [72], probabilistic models [67], or reinforcement learning [88].

Machine learning is also a rich source of complex data management problems: thus, the probabilities produced by a conditional random field [78] system result in probabilistic annotations that need to be properly modeled, stored, and queried.

Finally, complex data management also brings new twists to some classical machine learning problems. Consider for instance the area of active learning [85], a subfield of machine learning concerned with how to optimally use a (costly) oracle, in an interactive manner, to label training data that will be used to build a learning model, e.g., a classifier. In most of the active learning literature, the cost model is very basic (uniform or fixed-value costs), though some works [84] consider more realistic costs. Also, oracles are usually assumed to be perfect with only a few exceptions [62]. These assumptions usually break when applied to complex data management problems on real-world data, such as crowdsourcing.

Having situated Valda's research area within its broader scientific scope, we now move to the discussion of Valda's application domains.