--- res: bibo_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.@eng' bibo_authorlist: - foaf_Person: foaf_givenName: Krishnendu foaf_name: Chatterjee, Krishnendu foaf_surname: Chatterjee foaf_workInfoHomepage: http://www.librecat.org/personId=2E5DCA20-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-4561-241X - foaf_Person: foaf_givenName: Thomas A foaf_name: Henzinger, Thomas A foaf_surname: Henzinger foaf_workInfoHomepage: http://www.librecat.org/personId=40876CD8-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-2985-7724 - foaf_Person: foaf_givenName: Jan foaf_name: Otop, Jan foaf_surname: Otop foaf_workInfoHomepage: http://www.librecat.org/personId=2FC5DA74-F248-11E8-B48F-1D18A9856A87 bibo_doi: 10.4230/LIPIcs.CONCUR.2020.23 bibo_volume: 171 dct_date: 2020^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/18688969 - http://id.crossref.org/issn/9783959771603 dct_language: eng dct_publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik@ dct_title: Multi-dimensional long-run average problems for vector addition systems with states@ ...