## Abstract

One-counter nets (OCN) consist of a nondeterministic finite control and a single integer counter that cannot be fully tested for zero. They form a natural subclass of both One-Counter Automata, which allow zero-tests and Petri Nets/VASS, which allow multiple such weak counters. The trace inclusion problem has recently been shown to be undecidable for OCN. In this paper, we contrast the complexity of two natural restrictions which imply decidability.

We show that trace inclusion between a OCN and a deterministic OCN is NL-complete, even with arbitrary binary-encoded initial countervalues as part of the input. Secondly, we show that the the trace universality problem of nondeterministic OCN, which is equivalent to checking trace inclusion between a finite and a OCN-process, is Ackermann-complete.

We show that trace inclusion between a OCN and a deterministic OCN is NL-complete, even with arbitrary binary-encoded initial countervalues as part of the input. Secondly, we show that the the trace universality problem of nondeterministic OCN, which is equivalent to checking trace inclusion between a finite and a OCN-process, is Ackermann-complete.

Original language | English |
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Title of host publication | Reachability Problems |

Subtitle of host publication | 8th International Workshop, RP 2014, Oxford, UK, September 22-24, 2014. Proceedings |

Editors | Joël Ouaknine, Igor Potapov, James Worrell |

Place of Publication | Cham |

Publisher | Springer International Publishing |

Pages | 151-162 |

Number of pages | 12 |

ISBN (Electronic) | 978-3-319-11439-2 |

ISBN (Print) | 978-3-319-11438-5 |

DOIs | |

Publication status | Published - 2014 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer International Publishing |

Volume | 8762 |

ISSN (Print) | 0302-9743 |