Challenging Problems in Infinite-State Systems

ongoing

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.