Formalization of graph search algorithms and its applications

  • Mitsuharu Yamamoto
  • Koichi Takahashi
  • Masami Hagiya
  • Shin-ya Nishizaki
  • Tetsuo Tamai
Refereed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1479)


This paper describes a formalization of a class of fixed-point problems on graphs and its applications. This class captures several well-known graph theoretical problems such as those of shortest path type and for data flow analysis. An abstract solution algorithm of the fixed-point problem is formalized and its correctness is proved using a theorem proving system. Moreover, the validity of the A* algorithm, considered as a specialized version of the abstract algorithm, is proved by extending the proof of the latter. The insights we obtained through these formalizations are described. We also discuss the extension of this approach to the verification of model checking algorithms.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Mitsuharu Yamamoto
    • 1
  • Koichi Takahashi
    • 2
  • Masami Hagiya
    • 3
  • Shin-ya Nishizaki
    • 4
  • Tetsuo Tamai
    • 5
  1. 1.Faculty of ScienceChiba UniversityChibaJapan
  2. 2.Electrotechnical LaboratoryIbarakiJapan
  3. 3.Graduate School of ScienceThe University of TokyoTokyoJapan
  4. 4.Graduate School of Information Science and EngineeringTokyo Institute of TechnologyTokyoJapan
  5. 5.Graduate School of Arts and SciencesThe University of TokyoTokyoJapan

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