Alternation removal in Büchi automata

Udi Boker*, Orna Kupferman, Adin Rosenberg

*Corresponding author for this work

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

18 Scopus citations


Alternating automata play a key role in the automata-theoretic approach to specification, verification, and synthesis of reactive systems. Many algorithms on alternating automata, and in particular, their nonemptiness test, involve removal of alternation: a translation of the alternating automaton to an equivalent nondeterministic one. For alternating Büchi automata, the best known translation uses the "breakpoint construction" and involves an O(3 n ) state blow-up. The translation was described by Miyano and Hayashi in 1984, and is widely used since, in both theory and practice. Yet, the best known lower bound is only 2 n . In this paper we develop and present a complete picture of the problem of alternation removal in alternating Büchi automata. In the lower bound front, we show that the breakpoint construction captures the accurate essence of alternation removal, and provide a matching Ω(3 n ) lower bound. Our lower bound holds already for universal (rather than alternating) automata with an alphabet of a constant size. In the upper-bound front, we point to a class of alternating Büchi automata for which the breakpoint construction can be replaced by a simpler n2 n construction. Our class, of ordered alternating Büchi automata, strictly contains the class of very-weak alternating automata, for which an n2 n construction is known.

Original languageAmerican English
Title of host publicationAutomata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings
Number of pages12
EditionPART 2
StatePublished - 2010
Event37th International Colloquium on Automata, Languages and Programming, ICALP 2010 - Bordeaux, France
Duration: 6 Jul 201010 Jul 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 2
Volume6199 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference37th International Colloquium on Automata, Languages and Programming, ICALP 2010


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