{"day":"06","year":"2020","volume":171,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","language":[{"iso":"eng"}],"oa":1,"license":"https://creativecommons.org/licenses/by/3.0/","publication_status":"published","external_id":{"arxiv":["2007.08917"]},"doi":"10.4230/LIPIcs.CONCUR.2020.23","file":[{"success":1,"date_created":"2020-10-05T14:04:25Z","file_size":601231,"content_type":"application/pdf","checksum":"5039752f644c4b72b9361d21a5e31baf","date_updated":"2020-10-05T14:04:25Z","access_level":"open_access","file_name":"2020_LIPIcsCONCUR_Chatterjee.pdf","creator":"dernst","relation":"main_file","file_id":"8610"}],"date_updated":"2021-01-12T08:20:15Z","article_number":"23","conference":{"start_date":"2020-09-01","location":"Virtual","name":"CONCUR: Conference on Concurrency Theory","end_date":"2020-09-04"},"_id":"8600","publication":"31st International Conference on Concurrency Theory","publication_identifier":{"issn":["18688969"],"isbn":["9783959771603"]},"type":"conference","month":"08","date_published":"2020-08-06T00:00:00Z","file_date_updated":"2020-10-05T14:04:25Z","oa_version":"Published Version","date_created":"2020-10-04T22:01:36Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","has_accepted_license":"1","article_processing_charge":"No","status":"public","title":"Multi-dimensional long-run average problems for vector addition systems with states","ddc":["000"],"tmp":{"short":"CC BY (3.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)"},"intvolume":"       171","citation":{"apa":"Chatterjee, K., Henzinger, T. A., &#38; Otop, J. (2020). Multi-dimensional long-run average problems for vector addition systems with states. In <i>31st International Conference on Concurrency Theory</i> (Vol. 171). Virtual: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2020.23\">https://doi.org/10.4230/LIPIcs.CONCUR.2020.23</a>","mla":"Chatterjee, Krishnendu, et al. “Multi-Dimensional Long-Run Average Problems for Vector Addition Systems with States.” <i>31st International Conference on Concurrency Theory</i>, vol. 171, 23, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:<a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2020.23\">10.4230/LIPIcs.CONCUR.2020.23</a>.","ieee":"K. Chatterjee, T. A. Henzinger, and J. Otop, “Multi-dimensional long-run average problems for vector addition systems with states,” in <i>31st International Conference on Concurrency Theory</i>, Virtual, 2020, vol. 171.","chicago":"Chatterjee, Krishnendu, Thomas A Henzinger, and Jan Otop. “Multi-Dimensional Long-Run Average Problems for Vector Addition Systems with States.” In <i>31st International Conference on Concurrency Theory</i>, Vol. 171. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. <a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2020.23\">https://doi.org/10.4230/LIPIcs.CONCUR.2020.23</a>.","ama":"Chatterjee K, Henzinger TA, Otop J. Multi-dimensional long-run average problems for vector addition systems with states. In: <i>31st International Conference on Concurrency Theory</i>. Vol 171. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:<a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2020.23\">10.4230/LIPIcs.CONCUR.2020.23</a>","short":"K. Chatterjee, T.A. Henzinger, J. Otop, in:, 31st International Conference on Concurrency Theory, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.","ista":"Chatterjee K, Henzinger TA, Otop J. 2020. Multi-dimensional long-run average problems for vector addition systems with states. 31st International Conference on Concurrency Theory. CONCUR: Conference on Concurrency Theory, LIPIcs, vol. 171, 23."},"author":[{"last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","first_name":"Krishnendu"},{"first_name":"Thomas A","orcid":"0000-0002-2985-7724","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","full_name":"Henzinger, Thomas A","last_name":"Henzinger"},{"full_name":"Otop, Jan","last_name":"Otop","first_name":"Jan","id":"2FC5DA74-F248-11E8-B48F-1D18A9856A87"}],"alternative_title":["LIPIcs"],"department":[{"_id":"KrCh"},{"_id":"ToHe"}],"scopus_import":"1","quality_controlled":"1","project":[{"grant_number":"S 11407_N23","_id":"25832EC2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Rigorous Systems Engineering"},{"_id":"25F2ACDE-B435-11E9-9278-68D0E5697425","grant_number":"S11402-N23","name":"Rigorous Systems Engineering","call_identifier":"FWF"},{"_id":"25F42A32-B435-11E9-9278-68D0E5697425","grant_number":"Z211","name":"The Wittgenstein Prize","call_identifier":"FWF"}],"abstract":[{"text":"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.","lang":"eng"}]}