Seminars

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