---
_id: '10629'
abstract:
- lang: eng
text: "Product graphs arise naturally in formal verification and program analysis.
For example, the analysis of two concurrent threads requires the product of two
component control-flow graphs, and for language inclusion of deterministic automata
the product of two automata is constructed. In many cases, the component graphs
have constant treewidth, e.g., when the input contains control-flow graphs of
programs. We consider the algorithmic analysis of products of two constant-treewidth
graphs with respect to three classic specification languages, namely, (a) algebraic
properties, (b) mean-payoff properties, and (c) initial credit for energy properties.\r\nOur
main contributions are as follows. Consider a graph G that is the product of two
constant-treewidth graphs of size n each. First, given an idempotent semiring,
we present an algorithm that computes the semiring transitive closure of G in
time Õ(n⁴). Since the output has size Θ(n⁴), our algorithm is optimal (up to
polylog factors). Second, given a mean-payoff objective, we present an O(n³)-time
algorithm for deciding whether the value of a starting state is non-negative,
improving the previously known O(n⁴) bound. Third, given an initial credit for
energy objective, we present an O(n⁵)-time algorithm for computing the minimum
initial credit for all nodes of G, improving the previously known O(n⁸) bound.
At the heart of our approach lies an algorithm for the efficient construction
of strongly-balanced tree decompositions of constant-treewidth graphs. Given a
constant-treewidth graph G' of n nodes and a positive integer λ, our algorithm
constructs a binary tree decomposition of G' of width O(λ) with the property that
the size of each subtree decreases geometrically with rate (1/2 + 2^{-λ})."
alternative_title:
- LIPIcs
article_number: '42'
article_processing_charge: No
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. Quantitative verification on
product graphs of small treewidth. In: 41st IARCS Annual Conference on Foundations
of Software Technology and Theoretical Computer Science. Vol 213. Schloss
Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:10.4230/LIPIcs.FSTTCS.2021.42'
apa: 'Chatterjee, K., Ibsen-Jensen, R., & Pavlogiannis, A. (2021). Quantitative
verification on product graphs of small treewidth. In 41st IARCS Annual Conference
on Foundations of Software Technology and Theoretical Computer Science (Vol.
213). Virtual: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.FSTTCS.2021.42'
chicago: Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis.
“Quantitative Verification on Product Graphs of Small Treewidth.” In 41st IARCS
Annual Conference on Foundations of Software Technology and Theoretical Computer
Science, Vol. 213. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.
https://doi.org/10.4230/LIPIcs.FSTTCS.2021.42.
ieee: K. Chatterjee, R. Ibsen-Jensen, and A. Pavlogiannis, “Quantitative verification
on product graphs of small treewidth,” in 41st IARCS Annual Conference on Foundations
of Software Technology and Theoretical Computer Science, Virtual, 2021, vol.
213.
ista: 'Chatterjee K, Ibsen-Jensen R, Pavlogiannis A. 2021. Quantitative verification
on product graphs of small treewidth. 41st IARCS Annual Conference on Foundations
of Software Technology and Theoretical Computer Science. FSTTCS: Foundations of
Software Technology and Theoretical Computer Science, LIPIcs, vol. 213, 42.'
mla: Chatterjee, Krishnendu, et al. “Quantitative Verification on Product Graphs
of Small Treewidth.” 41st IARCS Annual Conference on Foundations of Software
Technology and Theoretical Computer Science, vol. 213, 42, Schloss Dagstuhl
- Leibniz-Zentrum für Informatik, 2021, doi:10.4230/LIPIcs.FSTTCS.2021.42.
short: K. Chatterjee, R. Ibsen-Jensen, A. Pavlogiannis, in:, 41st IARCS Annual Conference
on Foundations of Software Technology and Theoretical Computer Science, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2021.
conference:
end_date: 2021-12-17
location: Virtual
name: 'FSTTCS: Foundations of Software Technology and Theoretical Computer Science'
start_date: 2021-12-15
date_created: 2022-01-16T23:01:28Z
date_published: 2021-11-29T00:00:00Z
date_updated: 2022-01-17T10:39:40Z
day: '29'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.FSTTCS.2021.42
file:
- access_level: open_access
checksum: 71141acdeffa9056f24d6dbef952d254
content_type: application/pdf
creator: cchlebak
date_created: 2022-01-17T10:36:08Z
date_updated: 2022-01-17T10:36:08Z
file_id: '10633'
file_name: 2021_LIPIcs_Chatterjee.pdf
file_size: 891566
relation: main_file
success: 1
file_date_updated: 2022-01-17T10:36:08Z
has_accepted_license: '1'
intvolume: ' 213'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
publication: 41st IARCS Annual Conference on Foundations of Software Technology and
Theoretical Computer Science
publication_identifier:
isbn:
- 978-3-9597-7215-0
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantitative verification on product graphs of small treewidth
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 213
year: '2021'
...