Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F18%3A00100882" target="_blank" >RIV/00216224:14330/18:00100882 - isvavai.cz</a>

Result on the web

<a href="http://doi.acm.org/10.1145/3209108.3209191" target="_blank" >http://doi.acm.org/10.1145/3209108.3209191</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1145/3209108.3209191" target="_blank" >10.1145/3209108.3209191</a>

Result language

angličtina

Original language name

Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS

Original language description

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 kleq 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.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

10200 - Computer and information sciences

Project

<a href="/en/project/GA18-11193S" target="_blank" >GA18-11193S: Algorithms for Infinite-State Discrete Systems and Games</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

2018 33rd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

ISBN

9781450355834

ISSN

1043-6871

e-ISSN

—

Number of pages

10

Pages from-to

185-194

Publisher name

ACM

Place of publication

Oxford, England

Event location

Oxford, England

Event date

Jul 9, 2018

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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