Ideal decompositions for vector addition systems (invited talk).

*(English)*Zbl 1388.68199
Ollinger, Nicolas (ed.) et al., 33rd symposium on theoretical aspects of computer science, STACS 2016, Orléans, France, February 17–20, 2016. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik (ISBN 978-3-95977-001-9). LIPIcs – Leibniz International Proceedings in Informatics 47, Article 1, 13 p. (2016).

Summary: Vector addition systems, or equivalently Petri nets, are one of the most popular formal models for the representation and the analysis of parallel processes. Many problems for vector addition systems are known to be decidable thanks to the theory of well-structured transition systems. Indeed, vector addition systems with configurations equipped with the classical point-wise ordering are well-structured transition systems. Based on this observation, problems like coverability or termination can be proven decidable.

However, the theory of well-structured transition systems does not explain the decidability of the reachability problem. In this presentation, we show that runs of vector addition systems can also be equipped with a well quasi-order. This observation provides a unified understanding of the data structures involved in solving many problems for vector addition systems, including the central reachability problem.

For the entire collection see [Zbl 1338.68009].

However, the theory of well-structured transition systems does not explain the decidability of the reachability problem. In this presentation, we show that runs of vector addition systems can also be equipped with a well quasi-order. This observation provides a unified understanding of the data structures involved in solving many problems for vector addition systems, including the central reachability problem.

For the entire collection see [Zbl 1338.68009].

##### MSC:

68Q85 | Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.) |