---
_id: '5430'
abstract:
- lang: eng
text: We consider the core algorithmic problems related to verification of systems
with respect to three classical quantitative properties, namely, the mean- payoff
property, the ratio property, and the minimum initial credit for energy property.
The algorithmic problem given a graph and a quantitative property asks to compute
the optimal value (the infimum value over all traces) from every node of the graph.
We consider graphs with constant treewidth, and it is well-known that the control-flow
graphs of most programs have constant treewidth. Let n denote the number of nodes
of a graph, m the number of edges (for constant treewidth graphs m = O ( n ) )
and W the largest absolute value of the weights. Our main theoretical results
are as follows. First, for constant treewidth graphs we present an algorithm that
approximates the mean-payoff value within a mul- tiplicative factor of ∊ in time
O ( n · log( n/∊ )) and linear space, as compared to the classical algorithms
that require quadratic time. Second, for the ratio property we present an algorithm
that for constant treewidth graphs works in time O ( n · log( | a · b · n | ))
= O ( n · log( n · W )) , when the output is a b , as compared to the previously
best known algorithm with running time O ( n 2 · log( n · W )) . Third, for the
minimum initial credit problem we show that (i) for general graphs the problem
can be solved in O ( n 2 · m ) time and the associated decision problem can be
solved in O ( n · m ) time, improving the previous known O ( n 3 · m · log( n
· W )) and O ( n 2 · m ) bounds, respectively; and (ii) for constant treewidth
graphs we present an algorithm that requires O ( n · log n ) time, improving the
previous known O ( n 4 · log( n · W )) bound. We have implemented some of our
algorithms and show that they present a significant speedup on standard benchmarks.
alternative_title:
- IST Austria Technical Report
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Rasmus
full_name: Ibsen-Jensen, Rasmus
id: 3B699956-F248-11E8-B48F-1D18A9856A87
last_name: Ibsen-Jensen
orcid: 0000-0003-4783-0389
- first_name: Andreas
full_name: Pavlogiannis, Andreas
id: 49704004-F248-11E8-B48F-1D18A9856A87
last_name: Pavlogiannis
orcid: 0000-0002-8943-0722
citation:
ama: Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. *Faster Algorithms for Quantitative
Verification in Constant Treewidth Graphs*. IST Austria; 2015. doi:10.15479/AT:IST-2015-319-v1-1
apa: Chatterjee, K., Ibsen-Jensen, R., & Pavlogiannis, A. (2015). *Faster
algorithms for quantitative verification in constant treewidth graphs*. IST
Austria. https://doi.org/10.15479/AT:IST-2015-319-v1-1
chicago: Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis.
*Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs*.
IST Austria, 2015. https://doi.org/10.15479/AT:IST-2015-319-v1-1.
ieee: K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, *Faster algorithms
for quantitative verification in constant treewidth graphs*. IST Austria, 2015.
ista: Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2015. Faster algorithms for
quantitative verification in constant treewidth graphs, IST Austria, 31p.
mla: Chatterjee, Krishnendu, et al. *Faster Algorithms for Quantitative Verification
in Constant Treewidth Graphs*. IST Austria, 2015, doi:10.15479/AT:IST-2015-319-v1-1.
short: K. Chatterjee, R. Ibsen-Jensen, A. Pavlogiannis, Faster Algorithms for Quantitative
Verification in Constant Treewidth Graphs, IST Austria, 2015.
date_created: 2018-12-12T11:39:17Z
date_published: 2015-02-10T00:00:00Z
date_updated: 2021-01-12T08:02:17Z
day: '10'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.15479/AT:IST-2015-319-v1-1
file:
- access_level: open_access
checksum: 62c6ea01e342553dcafb88a070fb1ad5
content_type: application/pdf
creator: system
date_created: 2018-12-12T11:53:21Z
date_updated: 2020-07-14T12:46:52Z
file_id: '5482'
file_name: IST-2015-319-v1+1_long.pdf
file_size: 1089651
relation: main_file
file_date_updated: 2020-07-14T12:46:52Z
has_accepted_license: '1'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: '31'
publication_identifier:
issn:
- 2664-1690
publication_status: published
publisher: IST Austria
pubrep_id: '319'
related_material:
record:
- id: '1607'
relation: later_version
status: public
- id: '5437'
relation: later_version
status: public
status: public
title: Faster algorithms for quantitative verification in constant treewidth graphs
type: technical_report
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2015'
...