Seminars

Title: Managing structural and behavioral evolution in relational database: Application of Software Engineering techniques.
Abstract:

Relational databases play a central role in many information systems.
Their schemas usually contain structural and behavioral entity descriptions.
However, as any piece of software, they must continuously evolve to adapt to new
requirements of a world in constant change. From an evolution point of view,
problems are twofold: (1) relational database management systems do not allow
inconsistencies i.e., no entity can reference a non existing entity; (2) stored
procedures bodies are not described by meta-data i.e., DBMS as PostgreSQL
consider stored procedure bodies as plain text and references to entities are
unknown. As a consequence, evaluating the impact of an evolution of the database
schema is a difficult task. In this seminar, we present a semi-automatic
approach based on recommendations (sort of nested code transformations).
Recommendations are proposed to architects who select the ones fitting their
needs. Selected recommendations are then analysed and compiled to generate SQL
script respecting the constraints imposed by the RDBMS. To support
recommendations, we designed a meta-model for relational databases easing
computation of change impact. We performed an experiment to validate the
approach by reproducing a real evolution on a database. The results of our
experiment show that our approach is able to reproduce exactly a manual
modification in 75% less time.


Zoom link: univ-lille-fr.zoom.us/j/95419000064

Title: Can Earliest Query Answering on Nested Streams be achieved in Combined Linear Time?

Title: Regularizing the delay of enumeration algorithms
Zoom link: univ-lille-fr.zoom.us/j/95419000064
Abstract: Enumeration algorithms are algorithms whose goal is to output the set
of all solutions to a given problem. There exists different measures for the
quality of such algorithm, whose relevance depends on what the user wants to do
with the solutions set.

If the goal of the user is to explore some solutions or to transform the
solutions as they are outputted with a stream-like algorithm, a relevant measure
of the complexity of an enumeration algorithm is the delay between the output of
two distinct solutions. Following this line of thoughts, significant efforts
have been made by the community to design polynomial delay algorithms, that is,
algorithms whose delay between the output of two new solutions is polynomial in
the size of the input.

While this measure is interesting, it is not always completely necessary to have
a bound on the delay and it is enough to ask for a guarantee that running the
algorithm for O(t poly(n)) will result in the output of at least t solutions. Of
course, by storing each solution seen and outputting them regularly, one can
simulate a polynomial delay but if the number of solutions is large, it may
result in a blow up in the space used by the enumerator.

In this talk, we will present a new technique that allow to transform such
algorithm into polynomial delay algorithm using polynomial space.

This is joint work with Yann Strozecki.

Title: The planar geometry of first-order string transductions (joint work with Pierre Pradic)


Abstract:
hal.archives-ouvertes......ument

We propose a new machine model recognizing star-free languages, with a geometric flavor. Our starting point is the characterization of regular languages using two-way automata (2DFA). The idea is to take seriously the visual representations found throughout the literature of the behavior of a 2DFA on a word ; by putting a total order on the set of states, one can formally define what it means for such a behavior to be planar, in a sense analogous to the planarity of combinatorial maps. Star-free languages are then exactly the languages recognized by "planar 2DFA". We also show that the corresponding planar transducer model characterizes the class of first-order transductions (a.k.a. aperiodic regular functions). If time allows, the talk will briefly discuss the connections of this work with the non-commutative lambda-calculus (cf. our recent paper Aperiodicity in a non-commutative logic, ICALP'20).

Speaker: Nofar Carmeli (nofar.carme.li/)

Zoom link: univ-lille-fr.zoom.us/j/95419000064

Title: The Complexity of Answering Unions of Conjunctive Queries.

Abstract:
We discuss the fine-grained complexity of enumerating the answers to a query over a relational database. With the ideal guarantees, linear time is required before the first answer to read the input and determine its existence, and then we need to print the answers one by one. Consequently, we wish to identify the queries that can be solved with linear preprocessing time and constant or logarithmic delay between answers. A known dichotomy classifies CQs into those that admit such enumeration and those that do not. The computationally expensive component of query answering is joining tables, which can be done efficiently if and only if the join query is acyclic. However, the join query usually does not appear in a vacuum; for example, it may be part of a larger query, or it may be applied to a database with dependencies. We inspect how the complexity changes in these settings and chart the borders of tractability within. In addition, we consider the task of enumerating query answers with a uniformly random order, and we propose to do so using an efficient random-access structure for representing the set of answers. We also prove conditional lower bounds showing that our algorithms capture all tractable queries in some cases. Among our results, we show that a union of tractable conjunctive queries may be intractable w.r.t. random access; on the other hand, a union of intractable conjunctive queries may be tractable w.r.t. enumeration.

Title: Extracting nested relational queries from implicit definitions

Abstract:
arxiv.org/pdf/2005.06503.pdf

In this talk, I will present results obtained jointly with Michael
Benedikt establishing a connection between the Nested Relational
Calculus (NRC) and sets implicitly definable using Δ₀ formulas.

Call a formula φ(I,O) an implicit definition of the relation O(x,...) in
terms of I(y,...) if O is functionally determined by I: for every I, O,
O', if both φ(I,O) and φ(I,O') hold, then we have O ≡ O'. When φ is
first-order and I and O are relations over base sorts, then Beth's
definability theorem states that there is a first-order formula
ψ(I,x,...) corresponding to O whenever φ(I,O) holds. Further, this
explicit definition ψ can be effectively be computed from a sequent
calculus proof witnessing that φ is functional. This allows for
practical use of implicit definitions in the context of database
programming, as there is a well-established link between fragments of
explicitly FO definable relations and relational calculi.

NRC is a conservative extension of relational calculi from database
theory with limited powerset types in addition to tupling and anonymous
base types. NRC expressions thus not only encompass flat relations over
primitive datatypes like SQL but also nested collections, while
remaining useful in practice.

We extend the above correspondence between first-order logic and flat
relational queries to NRC and implicit definitions using set-theoretical
Δ₀ formulas over (typed) nested collection. Our proof of the equivalence
goes through a notion of Δ₀-interpretation and a generalization of Beth
definability for multi-sorted structures. This proof is non-constructive
and thus does not yield any useful algorithm for converting implicit
definitions into NRC terms. Using an approach more closely related to
proof-theoretic interpolation, we give a constructive proof of the
result restricted to intuitionistic provability, i.e, when the input
functionality proof π of φ(I,O) is carried out in intuitionistic logic.
Further, if π is cut-free, this can be done efficiently. Whether or not
there exists a polynomial-time procedure working with classical proofs
of functionality is still an open problem.

I will focus on the effective result for the talk, and if time allows,
discuss the difficulties with extending it to classical logic. I will
not assume any background in either database or model theory.