On Semantically-Deterministic Automata

Bader Abu Radi*, Orna Kupferman*

*Corresponding author for this work

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


Nondeterminism is a fundamental notion in Theoretical Computer Science. A nondeterministic automaton is semantically deterministic (SD) if different nondeterministic choices in the automaton lead to equivalent states. Semantic determinism is interesting as it is a natural relaxation of determinism, and as some applications of automata in formal methods require deterministic automata, yet in fact can use automata with some level of nondeterminism, tightly related to semantic determinism. In the context of finite words, semantic determinism coincides with determinism, in the sense that every pruning of an SD automaton to a deterministic one results in an equivalent automaton. We study SD automata on infinite words, focusing on Büchi, co-Büchi, and weak automata. We show that there, while semantic determinism does not increase the expressive power, the combinatorial and computational properties of SD automata are very different from these of deterministic automata. In particular, SD Büchi and co-Büchi automata are exponentially more succinct than deterministic ones (in fact, also exponentially more succinct than history-deterministic automata), their complementation involves an exponential blow up, and decision procedures for them like universality and minimization are PSPACE-complete. For weak automata, we show that while an SD weak automaton need not be pruned to an equivalent deterministic one, it can be determinized to an equivalent deterministic weak automaton with the same state space, implying also efficient complementation and decision procedures for SD weak automata.

Original languageAmerican English
Title of host publication50th International Colloquium on Automata, Languages, and Programming, ICALP 2023
EditorsKousha Etessami, Uriel Feige, Gabriele Puppis
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Number of pages20
ISBN (Electronic)9783959772785
StatePublished - Jul 2023
Event50th International Colloquium on Automata, Languages, and Programming, ICALP 2023 - Paderborn, Germany
Duration: 10 Jul 202314 Jul 2023

Publication series

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


Conference50th International Colloquium on Automata, Languages, and Programming, ICALP 2023

Bibliographical note

Publisher Copyright:
© Bader Abu Radi and Orna Kupferman.


  • Automata on infinite words
  • Decision procedures
  • Nondeterminism
  • Succinctness


Dive into the research topics of 'On Semantically-Deterministic Automata'. Together they form a unique fingerprint.

Cite this