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

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Formal Methods in Computer-Aided Design (FMCAD 2000)

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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’ 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.

This work was supported in part by SRC contract 98-DJ-620 and NSF grant CCR- 99-71195.

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Author information

Authors and Affiliations

  1. University of Colorado at Boulder, USA

    Roderick Bloem, Harold N. Gabow & Fabio Somenzi

Authors
  1. Roderick Bloem
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  2. Harold N. Gabow
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  3. Fabio Somenzi
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Editor information

Editors and Affiliations

  1. Austin Research Laboratories, IBM Corporation, Mail Stop 9460, Building 904 11501 Burnet Road, 78758, Austin, Texas, USA

    Warren A. Hunt Jr.

  2. Computer Science Department, Indiana University, Lindley Hall, 150 W. Woodlawn Avenue, 47405-7104, Bloomington, Indiana, USA

    Steven D. Johnson

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© 2000 Springer-Verlag Berlin Heidelberg

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Bloem, R., Gabow, H.N., Somenzi, F. (2000). An Algorithm for Strongly Connected Component Analysis in n log n Symbolic Steps. In: Hunt, W.A., Johnson, S.D. (eds) Formal Methods in Computer-Aided Design. FMCAD 2000. Lecture Notes in Computer Science, vol 1954. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40922-X_4

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  • DOI: https://doi.org/10.1007/3-540-40922-X_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41219-9

  • Online ISBN: 978-3-540-40922-9

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