--- _id: '143' abstract: - lang: eng text: 'Vector Addition Systems with States (VASS) provide a well-known and fundamental model for the analysis of concurrent processes, parameterized systems, and are also used as abstract models of programs in resource bound analysis. In this paper we study the problem of obtaining asymptotic bounds on the termination time of a given VASS. In particular, we focus on the practically important case of obtaining polynomial bounds on termination time. Our main contributions are as follows: First, we present a polynomial-time algorithm for deciding whether a given VASS has a linear asymptotic complexity. We also show that if the complexity of a VASS is not linear, it is at least quadratic. Second, we classify VASS according to quantitative properties of their cycles. We show that certain singularities in these properties are the key reason for non-polynomial asymptotic complexity of VASS. In absence of singularities, we show that the asymptotic complexity is always polynomial and of the form Θ(nk), for some integer k d, where d is the dimension of the VASS. We present a polynomial-time algorithm computing the optimal k. For general VASS, the same algorithm, which is based on a complete technique for the construction of ranking functions in VASS, produces a valid lower bound, i.e., a k such that the termination complexity is (nk). Our results are based on new insights into the geometry of VASS dynamics, which hold the potential for further applicability to VASS analysis.' alternative_title: - ACM/IEEE Symposium on Logic in Computer Science article_processing_charge: No author: - first_name: Tomáš full_name: Brázdil, Tomáš last_name: Brázdil - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Antonín full_name: Kučera, Antonín last_name: Kučera - first_name: Petr full_name: Novotny, Petr id: 3CC3B868-F248-11E8-B48F-1D18A9856A87 last_name: Novotny - first_name: Dominik full_name: Velan, Dominik last_name: Velan - first_name: Florian full_name: Zuleger, Florian last_name: Zuleger citation: ama: 'Brázdil T, Chatterjee K, Kučera A, Novotný P, Velan D, Zuleger F. Efficient algorithms for asymptotic bounds on termination time in VASS. In: Vol F138033. IEEE; 2018:185-194. doi:10.1145/3209108.3209191' apa: 'Brázdil, T., Chatterjee, K., Kučera, A., Novotný, P., Velan, D., & Zuleger, F. (2018). Efficient algorithms for asymptotic bounds on termination time in VASS (Vol. F138033, pp. 185–194). Presented at the LICS: Logic in Computer Science, Oxford, United Kingdom: IEEE. https://doi.org/10.1145/3209108.3209191' chicago: Brázdil, Tomáš, Krishnendu Chatterjee, Antonín Kučera, Petr Novotný, Dominik Velan, and Florian Zuleger. “Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS,” F138033:185–94. IEEE, 2018. https://doi.org/10.1145/3209108.3209191. ieee: 'T. Brázdil, K. Chatterjee, A. Kučera, P. Novotný, D. Velan, and F. Zuleger, “Efficient algorithms for asymptotic bounds on termination time in VASS,” presented at the LICS: Logic in Computer Science, Oxford, United Kingdom, 2018, vol. F138033, pp. 185–194.' ista: 'Brázdil T, Chatterjee K, Kučera A, Novotný P, Velan D, Zuleger F. 2018. Efficient algorithms for asymptotic bounds on termination time in VASS. LICS: Logic in Computer Science, ACM/IEEE Symposium on Logic in Computer Science, vol. F138033, 185–194.' mla: Brázdil, Tomáš, et al. Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS. Vol. F138033, IEEE, 2018, pp. 185–94, doi:10.1145/3209108.3209191. short: T. Brázdil, K. Chatterjee, A. Kučera, P. Novotný, D. Velan, F. Zuleger, in:, IEEE, 2018, pp. 185–194. conference: end_date: 2018-07-12 location: Oxford, United Kingdom name: 'LICS: Logic in Computer Science' start_date: 2018-07-09 date_created: 2018-12-11T11:44:51Z date_published: 2018-07-09T00:00:00Z date_updated: 2023-09-11T13:23:42Z day: '09' department: - _id: KrCh doi: 10.1145/3209108.3209191 ec_funded: 1 external_id: isi: - '000545262800020' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1804.10985 month: '07' oa: 1 oa_version: Preprint page: 185 - 194 project: - _id: 25892FC0-B435-11E9-9278-68D0E5697425 grant_number: ICT15-003 name: Efficient Algorithms for Computer Aided Verification - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 25832EC2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S 11407_N23 name: Rigorous Systems Engineering publication_identifier: isbn: - 978-1-4503-5583-4 publication_status: published publisher: IEEE publist_id: '7780' quality_controlled: '1' scopus_import: '1' status: public title: Efficient algorithms for asymptotic bounds on termination time in VASS type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: F138033 year: '2018' ...