A Hierarchy of Nondeterminism

Bader Abu Radi, Orna Kupferman, Ofer Leshkowitz

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

7 Scopus citations


We study three levels in a hierarchy of nondeterminism: A nondeterministic automaton A is determinizable by pruning (DBP) if we can obtain a deterministic automaton equivalent to A by removing some of its transitions. Then, A is good-for-games (GFG) if its nondeterministic choices can be resolved in a way that only depends on the past. Finally, A is semantically deterministic (SD) if different nondeterministic choices in A lead to equivalent states. Some applications of automata in formal methods require deterministic automata, yet in fact can use automata with some level of nondeterminism. For example, DBP automata are useful in the analysis of online algorithms, and GFG automata are useful in synthesis and control. For automata on finite words, the three levels in the hierarchy coincide. We study the hierarchy for Büchi, co-Büchi, and weak automata on infinite words. We show that the hierarchy is strict, study the expressive power of the different levels in it, as well as the complexity of deciding the membership of a language in a given level. Finally, we describe a probability-based analysis of the hierarchy, which relates the level of nondeterminism with the probability that a random run on a word in the language is accepting.

Original languageAmerican English
Title of host publication46th International Symposium on Mathematical Foundations of Computer Science, MFCS 2021
EditorsFilippo Bonchi, Simon J. Puglisi
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Number of pages21
ISBN (Electronic)9783959772013
StatePublished - 1 Aug 2021
Event46th International Symposium on Mathematical Foundations of Computer Science, MFCS 2021 - Tallinn, Estonia
Duration: 23 Aug 202127 Aug 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference46th International Symposium on Mathematical Foundations of Computer Science, MFCS 2021

Bibliographical note

Publisher Copyright:
© Bader Abu Radi, Orna Kupferman, and Ofer Leshkowitz; licensed under Creative Commons License CC-BY 4.0 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021).


  • Automata on infinite words
  • Complexity
  • Expressive power
  • Games


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