Efficient Algorithms for Asymptotic Bounds on Termination Time
in VASS

D 2018

Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS

BRÁZDIL, Tomáš, Krishnendu CHATTERJEE, Antonín KUČERA, Petr NOVOTNÝ, Dominik VELAN et. al.

Basic information

Original name

Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS

Authors

BRÁZDIL, Tomáš (203 Czech Republic, belonging to the institution), Krishnendu CHATTERJEE (356 India), Antonín KUČERA (203 Czech Republic, belonging to the institution), Petr NOVOTNÝ (203 Czech Republic), Dominik VELAN (203 Czech Republic, guarantor, belonging to the institution) and Florian ZULEGER (40 Austria)

Edition

Oxford, England, 2018 33rd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), p. 185-194, 10 pp. 2018

Publisher

ACM

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10200 1.2 Computer and information sciences

Country of publisher

United Kingdom of Great Britain and Northern Ireland

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

printed version "print"

References:

ACM Digital Library

RIV identification code

RIV/00216224:14330/18:00100882

Organization unit

Faculty of Informatics

ISBN

978-1-4503-5583-4

ISSN

DOI

http://dx.doi.org/10.1145/3209108.3209191

UT WoS

000545262800020

Keywords in English

vector addition systems with states; termination

Abstract

ORIG CZ

V originále

Vector Addition Systems with States (VASS) provide a well-known and fundamental model for the analysis of concurrent processes, parametrized 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 Theta(n^k), for some integer k\leq 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 Omega(n^k). Our results are based on new insights into the geometry of VASS dynamics, which hold the potential for further applicability to VASS analysis.

In Czech

V článku je studován problém asymptotického odhadu maximální délky výpočtu daného VASS systému.

Links

GA18-11193S, research and development project

Name: Algoritmy pro diskrétní systémy a hry s nekonečně mnoha stavy

Investor: Czech Science Foundation

MUNI/A/0854/2017, interní kód MU

Name: Rozsáhlé výpočetní systémy: modely, aplikace a verifikace VII.

Investor: Masaryk University, Category A

MUNI/A/1038/2017, interní kód MU

Name: Zapojení studentů Fakulty informatiky do mezinárodní vědecké komunity 18

Investor: Masaryk University, Category A

Citovat

BRÁZDIL, Tomáš, Krishnendu CHATTERJEE, Antonín KUČERA, Petr NOVOTNÝ, Dominik VELAN and Florian ZULEGER. Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS. In Anuj Dawar, Erich Gradel. 2018 33rd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). Oxford, England: ACM, 2018, p. 185-194. ISBN 978-1-4503-5583-4. Available from: https://dx.doi.org/10.1145/3209108.3209191.

@inproceedings{1413152,
   author = {Brázdil, Tomáš and Chatterjee, Krishnendu and Kučera, Antonín and Novotný, Petr and Velan, Dominik and Zuleger, Florian},
   address = {Oxford, England},
   booktitle = {2018 33rd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
   doi = {http://dx.doi.org/10.1145/3209108.3209191},
   editor = {Anuj Dawar, Erich Gradel},
   keywords = {vector addition systems with states; termination},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Oxford, England},
   isbn = {978-1-4503-5583-4},
   pages = {185-194},
   publisher = {ACM},
   title = {Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS},
   url = {http://doi.acm.org/10.1145/3209108.3209191},
   year = {2018}
}

TY  - JOUR
ID  - 1413152
AU  - Brázdil, Tomáš - Chatterjee, Krishnendu - Kučera, Antonín - Novotný, Petr - Velan, Dominik - Zuleger, Florian
PY  - 2018
TI  - Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS
PB  - ACM
CY  - Oxford, England
SN  - 9781450355834
KW  - vector addition systems with states
KW  - termination
UR  - http://doi.acm.org/10.1145/3209108.3209191
L2  - http://doi.acm.org/10.1145/3209108.3209191
N2  - Vector Addition Systems with States (VASS) provide a well-known and fundamental model for the analysis of concurrent processes, parametrized 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 Theta(n^k), for some integer k\leq 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 Omega(n^k). Our results are based on new insights into the geometry of VASS dynamics, which hold the potential for further applicability to VASS analysis.
ER  -

BRÁZDIL, Tomáš, Krishnendu CHATTERJEE, Antonín KUČERA, Petr NOVOTNÝ, Dominik VELAN and Florian ZULEGER. Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS. In Anuj Dawar, Erich Gradel. \textit{2018 33rd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)}. Oxford, England: ACM, 2018, p.~185-194. ISBN~978-1-4503-5583-4. Available from: https://dx.doi.org/10.1145/3209108.3209191.

Detailed Information on Publication Record