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Formalization of graph search algorithms and its applications

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Theorem Proving in Higher Order Logics (TPHOLs 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1479))

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Abstract

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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Author information

Authors and Affiliations

  1. Faculty of Science, Chiba University, 263-8522, Chiba, Japan

    Mitsuharu Yamamoto

  2. Electrotechnical Laboratory, Tsukuba, 305-8568, Ibaraki, Japan

    Koichi Takahashi

  3. Graduate School of Science, The University of Tokyo, 113-0033, Tokyo, Japan

    Masami Hagiya

  4. Graduate School of Information Science and Engineering, Tokyo Institute of Technology, Tokyo, Japan

    Shin-ya Nishizaki

  5. Graduate School of Arts and Sciences, The University of Tokyo, Tokyo, Japan

    Tetsuo Tamai

Authors
  1. Mitsuharu Yamamoto
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  2. Koichi Takahashi
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  3. Masami Hagiya
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  4. Shin-ya Nishizaki
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  5. Tetsuo Tamai
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Editor information

Jim Grundy Malcolm Newey

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© 1998 Springer-Verlag Berlin Heidelberg

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Yamamoto, M., Takahashi, K., Hagiya, M., Nishizaki, Sy., Tamai, T. (1998). Formalization of graph search algorithms and its applications. In: Grundy, J., Newey, M. (eds) Theorem Proving in Higher Order Logics. TPHOLs 1998. Lecture Notes in Computer Science, vol 1479. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055153

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  • DOI: https://doi.org/10.1007/BFb0055153

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64987-8

  • Online ISBN: 978-3-540-49801-8

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