On Minimal Odd Rankings for Büchi Complementation

  • Hrishikesh Karmarkar
  • Supratik Chakraborty
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5799)


We study minimal odd rankings (as defined by Kupferman and Vardi[KV01]) for run-DAGs of words in the complement of a nondeterministic Büchi automaton. We present an optimized version of the ranking based complementation construction of Friedgut, Kupferman and Vardi[FKV06] and Schewe’s[Sch09] variant of it, such that every accepting run of the complement automaton assigns a minimal odd ranking to the corresponding run-DAG. This allows us to determine minimally inessential ranks and redundant slices in ranking-based complementation constructions. We exploit this to reduce the size of the complement Büchi automaton by eliminating all redundant slices. We demonstrate the practical importance of this result through a set of experiments using the NuSMV model checker.


Level Ranking Complementation Construction Redundant Slice Assign Rank Subset Construction 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Hrishikesh Karmarkar
    • 1
  • Supratik Chakraborty
    • 1
  1. 1.Department of Computer Science and EngineeringIndian Institute of Technology Bombay 

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