I'm working on a problem where the formalism appears to be an abstraction of a kind of Petri net, and it is possible to construct an equivalent Petri net from this formalism with the same behavior. The Petri net that is constructed is bounded and deadlock free, and a transition is either $L0$-Live or $L1$-Live. So in this net, a transition fires only once or not at all.I've looked into the coverability of Petri nets and it appears that the coverability problem in general has $\text{EXPSPACE}$ complexity (https://www7.in.tum.de/~blondin/papers/BFHH16.pdf). However, I could not find any literature that relates the liveness of a Petri net to its coverability, and the impact on complexity. Is there any work that has looked into this?
Is there any work that relates the liveness of a Petri Net to the complexity of determining coverability?
complexity;covering problems;petri nets