Seminars

Speaker: Gabriel Bathie (perso.ens-lyon.fr/gabriel.bathie/)

Room: B21

Title: The complexity of Testing Regular Languages - Gabriel Bathie, Corto Mascle and Nathanaël Fijalkow (LaBRI, Université de Bordeaux)

Abstract:

Property testing is concerned with the design of algorithms making sublinear number of queries to distinguish whether the input satisfies a given property or is far from having this property.
A seminal paper of Alon, Krivelevich, Newman, and Szegedy in 2001 introduced property testing of formal languages: the goal is to determine whether an input word belongs to a given language, or is far from any word in that language (in terms of Hamming distance).
They constructed the first property testing algorithm for the class of all regular languages. Somewhat surprisingly, their algorithm uses a number of queries that does not depend on the length of the input word.
This opened up a line of work with improved complexity results and applications to streaming algorithms.
In this work, we show a trichotomy result: the class of regular languages can be divided into three classes, each of which is associated with an optimal testing complexity.
Our analysis yields effective characterizations for all three classes using so-called minimal blocking sequences, reasoning directly and combinatorially on automata.
This talk will give an overview of the methods used since the work of Alon et al. and highlight the main tools used for our combinatorial characterization.
Based on joint work with Corto Mascle and Nathanaël Fijalkow.

Speaker: Alexis de Colnet (www.ac.tuwien.ac.at/people/decolnet/)

Title: An FPRAS for #NFA and #nFBDD

Abstract:

#NFA is the problem of counting the words of a given length accepted by
a non-deterministic finite automaton (NFA). The problem is #P-hard but
the approximate variant admits polynomial-time randomized algorithms
(FPRAS, or fully-polynomial time randomized approximation schemes).
Arenas, Croquevielle, Jayaram and Riveros were the first to show that
#NFA admits an FPRAS and that this result extends to several other
counting problems, in fact all problems in the class SpanL. In this talk
we present another FPRAS for #NFA which applies to problems not covered
by Arenas et al.'s result. In particular, the FPRAS described in this
talk can be used for the problem of counting the satisfying assignments
of non-deterministic read-once branching programs (nFBDD).

Title: Efficient Optimization of Network Metrics in Large Uncertain
Graphs

Abstract: Graphs constitute an omnipresent data structure that can
model objects and their relationships in a wide variety of real-world
scenarios. The optimization of network metrics finds use in a plethora
of real-world applications. Most of the exact techniques for such tasks
turn out to be prohibitively time-consuming and memory-intensive for
the huge graphs that are usually encountered. Thus, there is a need for
efficient approximation algorithms. This talk focuses on the efficient
optimization of network metrics in large uncertain graphs, and
specifically the following three research problems. The first problem
aims to find, between a given pair of nodes in an uncertain graph, the
path having the highest probability of being a shortest path. The
second problem aims to find, in an uncertain graph, the subgraph having
the highest probability of being densest. The third problem is a novel
variant of the well-known opinion maximization problem where, given a
social network of users with real-valued opinions (about different
candidates), the goal is to choose the top-k seed users maximizing a
specific voting-based score at a given finite time horizon.
Best Regards,
Arkaprava

Titre: Scaling Neural Program Synthesis with Distribution-based Search
Abstract:
In this talk, we will discuss the problem of automatically constructing
computer programs from input-output examples, especially when the
target language is domain-specific and defined using a context-free
grammar. I will introduce a theoretical framework called
distribution-based search, discuss its challenges, and present several
search strategies based on learning the weights of a probabilistic
context-free grammar (PCFG) and then using this PCFG to enumerate the
most promising candidate programs efficiently.
The presentation will be based on the following paper published at
AAAI'2022: arxiv.org/abs/2110.12485
Joint work with Nathanaël Fijalkow, Théo Matricon, Kevin Ellis, Pierre
Ohlmann, Akarsh Potta

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.