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Challenging Problems in Infinite-State Systems

Project description

Fast algorithms and lower bounds for problems in infinite-state systems

The EU-funded INFSYS project aims to find solutions to challenging problems related to computational models called infinite-state systems. The project objectives concentrate on three main problems. The first one is reachability in Petri nets and vector addition systems. The study could lead to the design of faster algorithms that for a given system, defining the initial situation and the set of moves available, would answer the question about the possibility of transition to a specific end situation. The other two problems INFSYS will address are separation in automata theory and unambiguity in simple models.

Objective

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.

Host institution

UNIWERSYTET WARSZAWSKI
Net EU contribution
€ 1 340 406,00
Address
KRAKOWSKIE PRZEDMIESCIE 26/28
00-927 WARSZAWA
Poland

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Region
Makroregion województwo mazowieckie Warszawski stołeczny Miasto Warszawa
Activity type
Higher or Secondary Education Establishments
Links
Total cost
€ 1 340 406,00

Beneficiaries (1)