Minimization of Automata for Liveness Languages

Bader Abu Radi*, Orna Kupferman

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


While the minimization problem for deterministic Büchi word automata is known to be NP-complete, several fundamental problems around it are still open. This includes the complexity of minimzation for transition-based automata, where acceptance is defined with respect to the set of transitions that a run traverses infinitely often, and minimization for good-for-games (GFG) automata, where nondeterminism is allowed, yet has to be resolved in a way that only depends on the past. Of special interest in formal verification are liveness properties, which state that something “good” eventually happens. Liveness languages constitute a strict fragment of ω -regular languages, which suggests that minimization of automata recognizing liveness languages may be easier, as is the case for languages recognizable by weak automata, in particular safety languages. We define three classes of liveness, and study the minimization problem for automata recognizing languages in the classes. Our results refer to the basic minimization problem as well as to its extension to transition-based and GFG automata. In some cases, we provide bounds, and in others we provide connections between the different settings. Thus, our results are of practical interest and also improve our understanding of the (still very mysterious) minimization problem.

Original languageAmerican English
Title of host publicationAutomated Technology for Verification and Analysis - 20th International Symposium, ATVA 2022, Proceedings
EditorsAhmed Bouajjani, Lukáš Holík, Zhilin Wu
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages17
ISBN (Print)9783031199912
StatePublished - 2022
Event20th International Symposium on Automated Technology for Verification and Analysis, ATVA 2022 - Virtual, Online
Duration: 25 Oct 202228 Oct 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13505 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference20th International Symposium on Automated Technology for Verification and Analysis, ATVA 2022
CityVirtual, Online

Bibliographical note

Funding Information:
Supported by The Neubauer Foundation of Ph.D Fellowship.

Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.


  • Automata on infinite words
  • Büchi
  • Complexity
  • Good-for-games automata
  • Liveness
  • Minimization


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