On the Hereditary Properties of Modular Nets

Hereditary graph properties are those that can be inherited from the graph to all its subgraphs (such as planarity). Modular nets of active resources is a (Petri nets)-powerful formalism with simple modular syntax. Boundedness and liveness are fundamental semantic properties for Petri net models. It is shown that boundedness and liveness, being not hereditary in general, are downward-hereditary (net-to-subnet) and upward-hereditary (subnet-to-net) for the particular types of AR-subnets. It is also shown that boundedness is downward-hereditary and unboundedness is upward-hereditary for arbitrary subnets after a specific module interface transformation (so-called R-normalization).