The Büchi Complementation Saga

  • Moshe Y. Vardi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4393)


The complementation problem for nondeterministic word automata has numerous applications in formal verification. In particular, the language-containment problem, to which many verification problems are reduced, involves complementation. For automata on finite words, which correspond to safety properties, complementation involves determinization. The 2 n blow-up that is caused by the subset construction is justified by a tight lower bound. For Büchi automata on infinite words, which are required for the modeling of liveness properties, optimal complementation constructions are quite complicated, as the subset construction is not sufficient. We review here progress on this problem, which dates back to its introduction in Büchi’s seminal 1962 paper.


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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Moshe Y. Vardi
    • 1
  1. 1.Rice University, Department of Computer Science, Rice University, Houston, TX 77251-1892U.S.A.

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