License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
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DOI: 10.4230/LIPIcs.ICALP.2021.124
URN: urn:nbn:de:0030-drops-141930
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Chatterjee, Krishnendu ; Henzinger, Monika ; Kale, Sagar Sudhir ; Svozil, Alexander

Faster Algorithms for Bounded Liveness in Graphs and Game Graphs

LIPIcs-ICALP-2021-124.pdf (0.8 MB)


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

  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 =		{},
  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

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