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arXiv · 1511.04893

Context-Free Commutative Grammars with Integer Counters and Resets

Dmitry Chistikov·Christoph Haase·Simon Halfon
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Abstract

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 $\Pi_2^\text{P}$-complete for grammars with only one non-terminal symbol. Showing the lower bound for the latter result requires us to develop a novel $\Pi_2^\text{P}$-complete variant of the classic subset sum problem.

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Dmitry Chistikov, Christoph Haase, Simon Halfon. 2015-11-16. Context-Free Commutative Grammars with Integer Counters and Resets. https://arxiv.org/abs/1511.04893

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