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Structural analyses on the complexity of inverting functions

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Algorithms (SIGAL 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 450))

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Abstract

In this paper we investigate the complexity of inverting polynomial-time computable functions by methods developed in structural complexity theory. We first analyze upper bounds of the complexity of inverse functions by using complexity classes of functions. We prove the following: (1) NP/bit (the class of functions whose each bit is NP computable) is an upper bound for inverting honest and one-to-one functions, and (2) relative to almost all oracle, the class PF NPtt (the class of functions that are polynomial time computable by asking non-adaptive queries to an NP oracle) is an upper bound for inverting honest functions. Next we investigate relative complexity of inverse functions by using polynomial-time reducibility of functions. We prove that an honest function is NP/bit invertible if the class of its inverse functions possesses the least element under polynomial-time non-adaptive one-query reducibility.

(Extended Abstract)

watanabecs.titech.ac.jp

todacso.cs.uec.ac.jp

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Author information

Authors and Affiliations

  1. Department of Computer Science, Tokyo Institute of Technology, Meguro-ku, 152, Tokyo, Japan

    Osamu Watanabe

  2. Department of Computer Science, University of Electro-Communications, Chofu-shi, 182, Tokyo, Japan

    Seinosuke Toda

Authors
  1. Osamu Watanabe
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  2. Seinosuke Toda
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Editor information

Tetsuo Asano Toshihide Ibaraki Hiroshi Imai Takao Nishizeki

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Watanabe, O., Toda, S. (1990). Structural analyses on the complexity of inverting functions. In: Asano, T., Ibaraki, T., Imai, H., Nishizeki, T. (eds) Algorithms. SIGAL 1990. Lecture Notes in Computer Science, vol 450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52921-7_53

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  • DOI: https://doi.org/10.1007/3-540-52921-7_53

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52921-7

  • Online ISBN: 978-3-540-47177-6

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