Alternating Weak Automata from Universal Trees

Authors Laure Daviaud, Marcin Jurdziński, Karoliina Lehtinen

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Author Details

Laure Daviaud
  • City, University of London, UK
Marcin Jurdziński
  • University of Warwick, UK
Karoliina Lehtinen
  • University of Liverpool, UK


We thank Moshe Vardi for encouraging us to bring the state-space blow-up of alternating parity to alternating weak automata translation in line with the state-of-the-art complexity of solving parity games.

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Laure Daviaud, Marcin Jurdziński, and Karoliina Lehtinen. Alternating Weak Automata from Universal Trees. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


An improved translation from alternating parity automata on infinite words to alternating weak automata is given. The blow-up of the number of states is related to the size of the smallest universal ordered trees and hence it is quasi-polynomial, and it is polynomial if the asymptotic number of priorities is at most logarithmic in the number of states. This is an exponential improvement on the translation of Kupferman and Vardi (2001) and a quasi-polynomial improvement on the translation of Boker and Lehtinen (2018). Any slightly better such translation would (if - like all presently known such translations - it is efficiently constructive) lead to algorithms for solving parity games that are asymptotically faster in the worst case than the current state of the art (Calude, Jain, Khoussainov, Li, and Stephan, 2017; Jurdziński and Lazić, 2017; and Fearnley, Jain, Schewe, Stephan, and Wojtczak, 2017), and hence it would yield a significant breakthrough.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Algorithmic game theory
  • alternating automata
  • weak automata
  • Büchi automata
  • parity automata
  • parity games
  • universal trees


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