Seminars

Sujet: TBA

Titre: Direct Access for Conjunctive Queries with Negation
Abstract:
Direct Access is the operation of returning, given an index j, the jth answer of a conjunctive query on a given database for a given order. While this problem is #P-hard in general (wrt combined complexity), many conjunctive queries are structured enough so that for some lexicographical ordering of their answers, one can have a direct access to the answer set of a query Q that takes polylogarithmic time in the size of the database after a polynomial time precomputation. Previous work has precisely characterised the tractable classes and given fined-grained lower bounds on the time needed for precomputation depending on the structure of the query. We give a generalisation of these tractability results to the case of signed conjunctive queries, that is, conjunctive queries that may contain negative atoms. Our technique is based on solving the direct access task for a class of circuits that can represent relational data. Our result then follows from the fact that the tractable (signed) conjunctive queries can be transformed into polynomial size circuits. We recover the known tractable classes from the literature in the case of positive conjunctive queries using this technique and also discover new islands of tractability for signed conjunctive queries. In particular, our result generalises to the Direct Access Problem the known tractabilities of counting the number of answers to beta-acyclic negative queries and of deciding whether a negative query with bounded nested-width has an answer. This is joint work with Florent Capelli.

TBA

Title: Search-Based Regular Expression Inference on a GPU

Abstract: Regular expression inference (REI) is a supervised machine
learning and program synthesis problem that takes a cost metric for regular
expressions, and positive and negative examples of strings as input. It
outputs a regular expression that is precise (i.e., accepts all positive
and rejects all negative examples), and minimal w.r.t. to the cost metric.
We present a novel algorithm for REI over arbitrary alphabets that is
enumerative and trades off time for space. Our main algorithmic idea is to
implement the search space of regular expressions succinctly as a
contiguous matrix of bitvectors. Collectively, the bitvectors represent, as
characteristic sequences, all sub-languages of the infix-closure of the
union of positive and negative examples. Mathematically, this is a semiring
of (a variant of) formal power series. Infix-closure enables bottom-up
compositional construction of larger from smaller regular expressions using
the operations of our semiring. This minimises data movement and
data-dependent branching, hence maximises data-parallelism. In addition,
the infix-closure remains unchanged during the search, hence search can be
staged: first pre-compute various expensive operations, and then run the
compute intensive search process. We provide two C++ implementations, one
for general purpose CPUs and one for Nvidia GPUs (using CUDA). We benchmark
both on Google Colab Pro: the GPU implementation is on average over 1000x
faster than the CPU implementation on the hardest benchmarks.

Joint work with Mojtaba Valizadeh

Download: martinfriedrichberger.net/pldi2023.html

Speaker: Lê Thành Dũng Nguyễn, aka “Tito” — nguyentito.eu/

Title: Polyregular functions: some recent developments

Abstract:
The class of polyregular functions is composed of the string-to-string functions computed by pebble transducers. While this machine model (which extends two-way finite transducers) is two decades old, several alternative characterizations of polyregular functions have been discovered recently [Bojańczyk 2018; Bojańczyk, Kiefer & Lhote 2019], demonstrating their canonicity. The name comes from the polynomial bound on the growth rate of these functions: |f(w)| = |w|^O(1) where |w| is the length of the string w.

In this talk, after recalling this context, I will present some subsequent developments in which I have been involved:
* the subclass of comparison-free polyregular (or “polyblind”) functions, definable through a natural restriction of pebble transducers, which Pierre Pradic and I actually discovered while studying a linear λ-calculus;
* some results that either relate the growth rate of a polyregular function (comparison-free or not) to the “resources” needed to compute it, or show that there is no such relationship.

Speaker: Rémi Morvan — www.morvan.xyz/

Titre: Approximation and Semantic Tree-width of Conjunctive Regular Path Queries

Abstract:
We show that the problem of whether a query is equivalent to a query of tree-width k is decidable, for the class of Unions of Conjunctive Regular Path Queries with two-way navigation (UC2RPQs). A previous result by Barceló, Romero, and Vardi has shown decidability for the case k=1, and here we show that decidability in fact holds for any arbitrary k>1. The algorithm is in 2ExpSpace, but we show that the complexity drops to the second level of the polynomial hierarchy for a restricted but practically relevant case of queries obtained by only allowing simple regular expressions.
We also investigate the related problem of approximating a UC2RPQ by queries of small tree-width. We exhibit an algorithm which, for any fixed number k, builds the maximal under-approximation of tree-width k of a UC2RPQ. The maximal under-approximation of tree-width k of a query q is a query q' of tree-width k which is contained in q in a maximal and unique way, that is, such that for every query q'' of tree-width k, if q'' is contained in q then q'' is also contained in q'. Joint work with Diego Figueira.