Covering problems

In combinatorics and computer science, the covering problem is a type of general question: if a certain structure covers another, or how many structures are required to cover another?

For Petri nets, for example, the covering problem is defined as the question if for a given marking, there exists a run of the net, such that some larger (or equal) marking can be reached. Larger means here that all components are at least as large as the ones of the given marking and at least one one is properly larger.