The project INFSYS (Challenging Problems in Infinite-State Systems) focuses on a class of computational models called infinite-state systems. Similarly as in economy market models help understanding future prices or meteorological models predict future weather in computer science one uses computation models. This approach was for example applied by Intel company to check whether the processors they design do not have some fundamental flaws. However, the main motivation behind the project is a deep believe that understanding basics of nature may have a profound impact on the way people live. Therefore the INFSYS project aims at solving the most natural problems in the area of infinite-state systems with a lot of focus on mathematical elegance, which be belive is a kind of a witness that our research touches a fundamental topic.
There are three main topics of the project: reachability problems, separability problem and unambiguous systems. Below I focus on explaining the reachability problems, this is the largest part of the project and also the one where we managed to achieve major contributions.
The reachability problem asks whether in an infinite graph with a distinguished inital and final vertex there is a path between these vertices. If the graph is a model of a program, which starts in the initial vertex and the final vertex is some erroneous configuration then existence of a path means that there is a possible error in the program. Therefore the reachability problem can be relevant in applications. On the other hand it is the most fundamental problem one can ask for a class of systems. Gaining understanding on the complexity of it helps a lot for investigation of other problems.
In the project we work a lot on the reachability problem for vector addition systems. Vector addition systems (VAS) are computation models, which focus on modelling counters. On one hand the model of VAS is almost equivalent to the model of Petri nets, which is widely used in practial modelling of systems. On the other hand the mathematics of VAS is very interesting and elegant, but still very far from being understood. There are many fundamental problems in this field, which despite of a pretty simple formulations, are waiting to be solved for decades. In the INFSYS project we want to find novel techniques which will accelerate the progress on understanding the structure of VAS and in consequence deliver new notions and new algorithms for various fundamental problems.
