Descripción del proyecto
Límites inferiores y algoritmos rápidos para problemas en sistemas de estado infinito
El proyecto INFSYS, financiado con fondos europeos, tiene como objetivo encontrar soluciones a los problemas acuciantes relacionados con los modelos computacionales denominados sistemas de estado infinito. Los objetivos del proyecto se centrarán en tres problemas principales. El primero es la accesibilidad en sistemas de suma de vectores y redes de Petri. El estudio podría llevar al diseño de algoritmos más rápidos que, al definir la situación inicial y el conjunto de movimientos disponibles, respondería a la pregunta sobre la posibilidad de una transición a una situación final concreta para un sistema determinado. Los otros dos problemas que abordará INFSYS son la separación en la teoría de autómatas y la falta de ambigüedad en modelos simples.
Objetivo
Investigation of infinite state systems is an active field since the early days of computer science.
Despite of decades of research the most fundamental questions are not understood well
even for basic models using only counters or a stack.
The aim of the project is to provide solutions of the most challenging problems in the area.
The goals of the project are grouped in three tasks:
- The first goal in concerned with the reachability problem in Petri nets or Vector Addition Systems (VASes),
a classical problem of fundamental importance. Recently, in a breakthrough paper (awarded the Best Paper
Award at STOC 2019) with co-authors we have improved the lower bound for this problem from \expspace to \tower-hardness.
The main goal of this task is to establish exact complexity of the reachability problem.
- The second task focuses on separability problems, which ask about existence of simple classifiers.
The first main goal in this task is to prove decidability of an important problem of regular separability for languages of VASes, i.e.
the question whether for two given VAS languages there is a regular language including one of them and disjoint
from the other one.
Second main goal is to solve the word separating problem, namely to decide whether for each two words of length $n$
there exists a DFA with logarithmic number of states recognizing exactly one of them.
- Without doubt the role of nondeterminism is a key question in theoretical computer science.
The goal of this task is to study the related notion of unambiguity, which has very interesting properties, but
is much less understood. My plan is to study unambiguity in simple models.
The main goal here is to understand the complexity of the universality problem
of unambiguous variants of finite automata and their extensions.
Ámbito científico
Palabras clave
Programa(s)
Régimen de financiación
ERC-STG - Starting GrantInstitución de acogida
00-927 WARSZAWA
Polonia