Efficient algorithms for asymptotic bounds on termination time in VASS

T. Brázdil, K. Chatterjee, A. Kučera, P. Novotny, D. Velan, F. Zuleger, in:, IEEE, 2018, pp. 185–194.


Conference Paper | Published | English
Author
; ; ; ; ;
Department
Series Title
ACM/IEEE Symposium on Logic in Computer Science
Abstract
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.
Publishing Year
Date Published
2018-07-09
Volume
F138033
Page
185 - 194
Conference
LICS: Logic in Computer Science
Conference Location
Oxford, United Kingdom
Conference Date
2018-07-09 – 2018-07-12
IST-REx-ID

Cite this

Brázdil T, Chatterjee K, Kučera A, Novotny 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
Brázdil, T., Chatterjee, K., Kučera, A., Novotny, 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
Brázdil, Tomáš, Krishnendu Chatterjee, Antonín Kučera, Petr Novotny, 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.
T. Brázdil, K. Chatterjee, A. Kučera, P. Novotny, 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.
Brázdil T, Chatterjee K, Kučera A, Novotny 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.
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.

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