2026-07-22T12:14:55Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12835 2024-03-06T10:50:48Z ddc:004 open_access

Multi-Dimensional Long-Run Average Problems for Vector Addition Systems with States Chatterjee, Krishnendu Henzinger, Thomas A. Otop, Jan vector addition systems mean-payoff multidimension probabilistic semantics 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Krishnendu Chatterjee and Thomas A. Henzinger and Jan Otop 2020 Is Part Of LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CONCUR.2020.23 urn:nbn:de:0030-drops-128359 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.23 eng https://creativecommons.org/licenses/by/3.0/legalcode