Application and Theory of Petri Nets and Concurrency . PETRI NETS 2013

Preface It is already a tradition to select papers from the annual PETRI NETS conference for a special issue of Fundamenta Informaticae. This volume presents six papers that extend or combine seven papers from the 34th International Conference on Application and Theory of Petri Nets and Concurrency which took place at the Università degli Studi di Milano-Bicocca in June 2013. The program committee chairs of the conference invited the respective authors to revise and extend their contributions for this special issue. The main topic discussed at the PETRI NETS conferences is of course Petri net theory, with a particular emphasis on application. However, as the suffix " and Concurrency " indicates, the conference is also open to other approaches to concurrency. Such contributions may be concerned with, e.g., the relationship between Petri nets and other formalisms, or extensions of the Petri net formalism. belongs to the latter category. Whereas transitions of usual Petri nets can only move single tokens, the firing rule of Continuous Petri Nets allows to move any positive real-valued multiple of tokens. Consequently, not only reachable markings are considered, but also limits of reachable markings after infinite occurrence sequences. Major contributions of this paper are improved complexity bounds for the most important Petri net properties, here transferred to Continuous Petri nets. The conference version of this paper received the Outstanding Paper Award from the program committee. Also the second paper ω-Petri Nets: Algorithms and Complexity deals with an extension of the Petri net firing rule. introduce and study ω-Petri nets, in which arcs may be annotated by ω with the semantics that, by firing the adjacent transition, any number of tokens can flow through this arc. Algorithms are proposed for verification problems like reachability, boundedness, covering, and termination. In addition, complexity and decidability results are provided for this net class, also when extended with reset and transfer arcs. The next two papers are typical Petri net theory contributions.