---
_id: '10054'
abstract:
- lang: eng
text: 'Graphs and games on graphs are fundamental models for the analysis of reactive
systems, in particular, for model-checking and the synthesis of reactive systems.
The class of ω-regular languages provides a robust specification formalism for
the desired properties of reactive systems. In the classical infinitary formulation
of the liveness part of an ω-regular specification, a "good" event must happen
eventually without any bound between the good events. A stronger notion of liveness
is bounded liveness, which requires that good events happen within d transitions.
Given a graph or a game graph with n vertices, m edges, and a bounded liveness
objective, the previous best-known algorithmic bounds are as follows: (i) O(dm)
for graphs, which in the worst-case is O(n³); and (ii) O(n² d²) for games on graphs.
Our main contributions improve these long-standing algorithmic bounds. For graphs
we present: (i) a randomized algorithm with one-sided error with running time
O(n^{2.5} log n) for the bounded liveness objectives; and (ii) a deterministic
linear-time algorithm for the complement of bounded liveness objectives. For games
on graphs, we present an O(n² d) time algorithm for the bounded liveness objectives.'
acknowledgement: 'Krishnendu Chatterjee: Supported by the ERC CoG 863818 (ForM-SMArt).
Monika Henzinger: Supported by the Austrian Science Fund (FWF) and netIDEE SCIENCE
project P 33775-N. Sagar Sudhir Kale: Partially supported by the Vienna Science
and Technology Fund (WWTF) through project ICT15-003. Alexander Svozil: Fully supported
by the Vienna Science and Technology Fund (WWTF) through project ICT15-003.'
alternative_title:
- LIPIcs
article_number: '124'
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: Monika H
full_name: Henzinger, Monika H
id: 540c9bbd-f2de-11ec-812d-d04a5be85630
last_name: Henzinger
orcid: 0000-0002-5008-6530
- first_name: Sagar Sudhir
full_name: Kale, Sagar Sudhir
last_name: Kale
- first_name: Alexander
full_name: Svozil, Alexander
last_name: Svozil
citation:
ama: 'Chatterjee K, Henzinger MH, Kale SS, Svozil A. Faster algorithms for bounded
liveness in graphs and game graphs. In: 48th International Colloquium on Automata,
Languages, and Programming. Vol 198. Schloss Dagstuhl - Leibniz Zentrum für
Informatik; 2021. doi:10.4230/LIPIcs.ICALP.2021.124'
apa: 'Chatterjee, K., Henzinger, M. H., Kale, S. S., & Svozil, A. (2021). Faster
algorithms for bounded liveness in graphs and game graphs. In 48th International
Colloquium on Automata, Languages, and Programming (Vol. 198). Glasgow, Scotland:
Schloss Dagstuhl - Leibniz Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ICALP.2021.124'
chicago: Chatterjee, Krishnendu, Monika H Henzinger, Sagar Sudhir Kale, and Alexander
Svozil. “Faster Algorithms for Bounded Liveness in Graphs and Game Graphs.” In
48th International Colloquium on Automata, Languages, and Programming,
Vol. 198. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. https://doi.org/10.4230/LIPIcs.ICALP.2021.124.
ieee: K. Chatterjee, M. H. Henzinger, S. S. Kale, and A. Svozil, “Faster algorithms
for bounded liveness in graphs and game graphs,” in 48th International Colloquium
on Automata, Languages, and Programming, Glasgow, Scotland, 2021, vol. 198.
ista: 'Chatterjee K, Henzinger MH, Kale SS, Svozil A. 2021. Faster algorithms for
bounded liveness in graphs and game graphs. 48th International Colloquium on Automata,
Languages, and Programming. ICALP: International Colloquium on Automata, Languages,
and Programming, LIPIcs, vol. 198, 124.'
mla: Chatterjee, Krishnendu, et al. “Faster Algorithms for Bounded Liveness in Graphs
and Game Graphs.” 48th International Colloquium on Automata, Languages, and
Programming, vol. 198, 124, Schloss Dagstuhl - Leibniz Zentrum für Informatik,
2021, doi:10.4230/LIPIcs.ICALP.2021.124.
short: K. Chatterjee, M.H. Henzinger, S.S. Kale, A. Svozil, in:, 48th International
Colloquium on Automata, Languages, and Programming, Schloss Dagstuhl - Leibniz
Zentrum für Informatik, 2021.
conference:
end_date: 2021-07-16
location: Glasgow, Scotland
name: 'ICALP: International Colloquium on Automata, Languages, and Programming'
start_date: 2021-07-12
date_created: 2021-09-27T14:33:15Z
date_published: 2021-07-02T00:00:00Z
date_updated: 2025-07-14T09:10:08Z
day: '02'
ddc:
- '000'
department:
- _id: KrCh
doi: 10.4230/LIPIcs.ICALP.2021.124
ec_funded: 1
file:
- access_level: open_access
checksum: 5a3fed8dbba8c088cbeac1e24cc10bc5
content_type: application/pdf
creator: cchlebak
date_created: 2021-10-01T08:49:26Z
date_updated: 2021-10-01T08:49:26Z
file_id: '10062'
file_name: 2021_LIPIcs_Chatterjee.pdf
file_size: 854576
relation: main_file
success: 1
file_date_updated: 2021-10-01T08:49:26Z
has_accepted_license: '1'
intvolume: ' 198'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 0599E47C-7A3F-11EA-A408-12923DDC885E
call_identifier: H2020
grant_number: '863818'
name: 'Formal Methods for Stochastic Models: Algorithms and Applications'
publication: 48th International Colloquium on Automata, Languages, and Programming
publication_identifier:
isbn:
- 978-3-95977-195-5
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
status: public
title: Faster algorithms for bounded liveness in graphs and game graphs
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: 6785fbc1-c503-11eb-8a32-93094b40e1cf
volume: 198
year: '2021'
...