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Formal Methods in System Design

, Volume 28, Issue 1, pp 37–56 | Cite as

An Algorithm for Strongly Connected Component Analysis in n log n Symbolic Steps

  • Roderick BloemEmail author
  • Harold N. Gabow
  • Fabio Somenzi
Article

Abstract

We present a symbolic algorithm for strongly connected component decomposition. The algorithm performs Θ(n log n) image and preimage computations in the worst case, where n is the number of nodes in the graph. This is an improvement over the previously known quadratic bound. The algorithm can be used to decide emptiness of Büchi automata with the same complexity bound, improving Emerson and Lei's quadratic bound, and emptiness of Streett automata, with a similar bound in terms of nodes. It also leads to an improved procedure for the generation of nonemptiness witnesses.

Keywords

symbolic algorithms strongly connected components binary decision diagrams language emptiness Büchi automata Streett automata model checking depth-first search breadth-first search 

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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • Roderick Bloem
    • 1
    Email author
  • Harold N. Gabow
    • 2
  • Fabio Somenzi
    • 2
  1. 1.Graz University of TechnologyAustria
  2. 2.University of ColoradoBoulder

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