Multi-dimensional long-run average problems for vector addition systems with states

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Series Title
LIPIcs
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.
Publishing Year
Date Published
2020-08-06
Proceedings Title
31st International Conference on Concurrency Theory
Publisher
Schloss Dagstuhl - Leibniz-Zentrum für Informatik
Volume
171
Article Number
23
Conference
CONCUR: Conference on Concurrency Theory
Conference Location
Virtual
Conference Date
2020-09-01 – 2020-09-04
ISSN
IST-REx-ID
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Access Level
OA Open Access
Date Uploaded
2020-10-05
MD5 Checksum
5039752f644c4b72b9361d21a5e31baf


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arXiv 2007.08917

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