Context-free commutative grammars with integer counters and resets

We study the computational complexity of reachability, coverability and inclusion for extensions of context-free commutative grammars with integer counters and reset operations on them. Those grammars can alternatively be viewed as an extension of communication-free Petri nets. Our main results are that reachability and coverability are inter-reducible and both NP-complete. In particular, this class of commutative grammars enjoys semi-linear reachability sets. We also show that the inclusion problem is, in general, coNEXP-complete and already Π2P-complete for grammars with only one non-terminal symbol. Showing the lower bound for the latter result requires us to develop a novel Π2P-complete variant of the classic subset sum problem.