License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2021.124
URN: urn:nbn:de:0030-drops-141930
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14193/
Chatterjee, Krishnendu ;
Henzinger, Monika ;
Kale, Sagar Sudhir ;
Svozil, Alexander
Faster Algorithms for Bounded Liveness in Graphs and Game Graphs
Abstract
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.
BibTeX - Entry
@InProceedings{chatterjee_et_al:LIPIcs.ICALP.2021.124,
author = {Chatterjee, Krishnendu and Henzinger, Monika and Kale, Sagar Sudhir and Svozil, Alexander},
title = {{Faster Algorithms for Bounded Liveness in Graphs and Game Graphs}},
booktitle = {48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
pages = {124:1--124:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-195-5},
ISSN = {1868-8969},
year = {2021},
volume = {198},
editor = {Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/14193},
URN = {urn:nbn:de:0030-drops-141930},
doi = {10.4230/LIPIcs.ICALP.2021.124},
annote = {Keywords: Graphs, Game Graphs, B\"{u}chi}
}
|
Keywords: |
|
Graphs, Game Graphs, Büchi |
|
Collection: |
|
48th International Colloquium on Automata, Languages, and Programming (ICALP 2021) |
|
Issue Date: |
|
2021 |
|
Date of publication: |
|
02.07.2021 |
