License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2020.23
URN: urn:nbn:de:0030-drops-128359
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12835/
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Chatterjee, Krishnendu ; Henzinger, Thomas A. ; Otop, Jan

Multi-Dimensional Long-Run Average Problems for Vector Addition Systems with States

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LIPIcs-CONCUR-2020-23.pdf (0.6 MB)


Abstract

A vector addition system with states (VASS) consists of a finite set of states and counters. A transition changes the current state to the next state, and every counter is either incremented, or decremented, or left unchanged. A state and value for each counter is a configuration; and a computation is an infinite sequence of configurations with transitions between successive configurations. A probabilistic VASS consists of a VASS along with a probability distribution over the transitions for each state. Qualitative properties such as state and configuration reachability have been widely studied for VASS. In this work we consider multi-dimensional long-run average objectives for VASS and probabilistic VASS. For a counter, the cost of a configuration is the value of the counter; and the long-run average value of a computation for the counter is the long-run average of the costs of the configurations in the computation. The multi-dimensional long-run average problem given a VASS and a threshold value for each counter, asks whether there is a computation such that for each counter the long-run average value for the counter does not exceed the respective threshold. For probabilistic VASS, instead of the existence of a computation, we consider whether the expected long-run average value for each counter does not exceed the respective threshold. Our main results are as follows: we show that the multi-dimensional long-run average problem (a) is NP-complete for integer-valued VASS; (b) is undecidable for natural-valued VASS (i.e., nonnegative counters); and (c) can be solved in polynomial time for probabilistic integer-valued VASS, and probabilistic natural-valued VASS when all computations are non-terminating.

BibTeX - Entry

@InProceedings{chatterjee_et_al:LIPIcs:2020:12835,
  author =	{Krishnendu Chatterjee and Thomas A. Henzinger and Jan Otop},
  title =	{{Multi-Dimensional Long-Run Average Problems for Vector Addition Systems with States}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{23:1--23:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Igor Konnov and Laura Kov{\'a}cs},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12835},
  URN =		{urn:nbn:de:0030-drops-128359},
  doi =		{10.4230/LIPIcs.CONCUR.2020.23},
  annote =	{Keywords: vector addition systems, mean-payoff, multidimension, probabilistic semantics}
}

Keywords: vector addition systems, mean-payoff, multidimension, probabilistic semantics
Collection: 31st International Conference on Concurrency Theory (CONCUR 2020)
Issue Date: 2020
Date of publication: 26.08.2020


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