Weak Alternating Automata Are Not that Weak

Orna Kupferman, Moshe Y. Vardi

Research output: Contribution to journalArticlepeer-review

171 Scopus citations


Automata on infinite words are used for specification and verification of nonterminating programs. Different types of automata induce different levels of expressive power, of succinctness, and of complexity. Alternating automata have both existential and universal branching modes and are particularly suitable for specification of programs. In a weak alternating automaton, the state space is partitioned into partially ordered sets, and the automaton can proceed from a certain set only to smaller sets. Reasoning about weak alternating automata is easier than reasoning about alternating automata with no restricted structure. Known translations of alternating automata to weak alternating automata involve determinization, and therefore involve a double-exponential blow-up. In this paper we describe a quadratic translation, which circumvents the need for determinization, of Büchi and co-Büchi alternating automata to weak alternating automata. Beyond the independent interest of such a translation, it gives rise to a simple complementation algorithm for nondeterministic Büchi automata.

Original languageAmerican English
Pages (from-to)408-429
Number of pages22
JournalACM Transactions on Computational Logic
Issue number3
StatePublished - 1 Jul 2001


  • Theory
  • Verification
  • Weak alternating automata
  • complementation


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