Context-free commutative grammars with integer counters and resets

• Published in: Theoretical computer science Vol. 735; pp. 147 - 161
• Main Authors: Chistikov, Dmitry, Haase, Christoph, Halfon, Simon
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 29.07.2018; Elsevier
• Subjects: Communication-free Petri nets; Computer Science; Context-free commutative grammars; Presburger arithmetic; Reset nets; Subset sum; Vector addition systems with states; Vector addition systems with states; Communication-free Petri nets; Reset nets; Context-free commutative grammars; Presburger arithmetic; Subset sum
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2016.06.017

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.