  The coverability and boundedness problems for Petri nets are known to be
Expspace-complete. Given a Petri net, we associate a graph with it. With the
vertex cover number k of this graph and the maximum arc weight W as parameters,
we show that coverability and boundedness are in ParaPspace. This means that
these problems can be solved in space O(ef(k,W)poly(n)), where ef(k,W) is some
exponential function and poly(n) is some polynomial in the size of the input.
We then extend the ParaPspace result to model checking a logic that can express
some generalizations of coverability and boundedness.
