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: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12835/
Chatterjee, Krishnendu ;
Henzinger, Thomas A. ;
Otop, Jan
Multi-Dimensional Long-Run Average Problems for Vector Addition Systems with States
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 |
