Hasse Diagram Generators and Petri Nets

In [LJ06] Lorenz and Juh´as raised the question of whether there exists a suitable formalism for the representation of infinite families of partial orders generated by Petri nets. Restricting ourselves to bounded p/t-nets, we propose Hasse diagram generators as an answer. We show that Hasse diagram generators are expressive enough to represent the partial order language of any bounded p/t net. We prove as well that it is decidable both whether the (possible infinite) family of partial orders represented by a given Hasse diagram generator is included on the partial order language of a given p/t-net and whether their intersection is empty. Based on this decidability result, we prove that the partial order languages of two given Petri nets can be effectively compared with respect to inclusion. Finally we address the synthesis of k-safe p/t-nets from Hasse diagram generators. Key words: Causality/partial order theory of concurrency.

• Type: Conference
• Year: 2009
• Where: APN
• Authors: Mateus de Oliveira Oliveira
• Keywords: APN 2009, Artificial Intelligence, Hasse Diagram Generators, Partial Order, Partial Order Languages