---
_id: '1607'
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 multiplicative factor of ϵ in time O(n⋅log(n/ϵ))
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|))=O(n⋅log(n⋅W)), when the output
is ab, as compared to the previously best known algorithm with running time O(n2⋅log(n⋅W)).
Third, for the minimum initial credit problem we show that (i) for general graphs
the problem can be solved in O(n2⋅m) time and the associated decision problem
can be solved in O(n⋅m) time, improving the previous known O(n3⋅m⋅log(n⋅W)) and
O(n2⋅m) bounds, respectively; and (ii) for constant treewidth graphs we present
an algorithm that requires O(n⋅logn) time, improving the previous known O(n4⋅log(n⋅W))
bound. We have implemented some of our algorithms and show that they present a
significant speedup on standard benchmarks.
acknowledgement: 'The research was partly supported by Austrian Science Fund (FWF)
Grant No P23499- N23, FWF NFN Grant No S11407-N23 (RiSE/SHiNE), ERC Start grant
(279307: Graph Games), and Microsoft faculty fellows award.'
alternative_title:
- LNCS
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. In: Vol 9206. Springer; 2015:140-157.
doi:10.1007/978-3-319-21690-4_9'
apa: 'Chatterjee, K., Ibsen-Jensen, R., & Pavlogiannis, A. (2015). Faster algorithms
for quantitative verification in constant treewidth graphs (Vol. 9206, pp. 140–157).
Presented at the CAV: Computer Aided Verification, San Francisco, CA, USA: Springer.
https://doi.org/10.1007/978-3-319-21690-4_9'
chicago: Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis.
“Faster Algorithms for Quantitative Verification in Constant Treewidth Graphs,”
9206:140–57. Springer, 2015. https://doi.org/10.1007/978-3-319-21690-4_9.
ieee: 'K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, “Faster algorithms for
quantitative verification in constant treewidth graphs,” presented at the CAV:
Computer Aided Verification, San Francisco, CA, USA, 2015, vol. 9206, pp. 140–157.'
ista: 'Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2015. Faster algorithms for
quantitative verification in constant treewidth graphs. CAV: Computer Aided Verification,
LNCS, vol. 9206, 140–157.'
mla: Chatterjee, Krishnendu, et al. *Faster Algorithms for Quantitative Verification
in Constant Treewidth Graphs*. Vol. 9206, Springer, 2015, pp. 140–57, doi:10.1007/978-3-319-21690-4_9.
short: K. Chatterjee, R. Ibsen-Jensen, A. Pavlogiannis, in:, Springer, 2015, pp.
140–157.
conference:
end_date: 2015-07-24
location: San Francisco, CA, USA
name: 'CAV: Computer Aided Verification'
start_date: 2015-07-18
corr_author: '1'
date_created: 2018-12-11T11:52:59Z
date_published: 2015-07-16T00:00:00Z
date_updated: 2024-10-09T20:57:31Z
day: '16'
department:
- _id: KrCh
doi: 10.1007/978-3-319-21690-4_9
ec_funded: 1
intvolume: ' 9206'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1504.07384
month: '07'
oa: 1
oa_version: Preprint
page: 140 - 157
project:
- _id: 2584A770-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P 23499-N23
name: Modern Graph Algorithmic Techniques in Formal Verification
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 2581B60A-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '279307'
name: 'Quantitative Graph Games: Theory and Applications'
- _id: 2587B514-B435-11E9-9278-68D0E5697425
name: Microsoft Research Faculty Fellowship
publication_status: published
publisher: Springer
publist_id: '5560'
quality_controlled: '1'
related_material:
record:
- id: '5430'
relation: earlier_version
status: public
- id: '5437'
relation: earlier_version
status: public
- id: '821'
relation: dissertation_contains
status: public
scopus_import: 1
status: public
title: Faster algorithms for quantitative verification in constant treewidth graphs
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 9206
year: '2015'
...