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...
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Published in | Theoretical computer science Vol. 735; pp. 147 - 161 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
29.07.2018
Elsevier |
Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 0304-3975 1879-2294 |
DOI: | 10.1016/j.tcs.2016.06.017 |