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Random Access to Advice Strings and Collapsing Results

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Book cover Algorithms and Computation (ISAAC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3341))

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Abstract

We propose a model of computation where a Turing machine is given random access to an advice string. With random access, an advice string of exponential length becomes meaningful for polynomially bounded complexity classes. We compare the power of complexity classes under this model. It gives a more stringent notion than the usual model of computation with relativization. Under this model of random access, we prove that there exist advice strings such that the Polynomial-time Hierarchy PH and Parity Polynomial-time \(\bigoplus\)P all collapse to P. Our main proof technique uses the decision tree lower bounds for constant depth circuits [Yao85, Cai86,Hås86]and the algebraic machinery of Razborov and Smolensky [Raz87, Smo87].

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Author information

Authors and Affiliations

  1. Computer Sci. Dept., Univ. of Wisconsin, Madison, WI, 53706, USA

    Jin-Yi Cai

  2. Dept. of Math. and Comp. Sci., Tokyo Inst. of Technology,  

    Osamu Watanabe

Authors
  1. Jin-Yi Cai
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  2. Osamu Watanabe
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Fudan University, 200433, Shanghai, China

    Rudolf Fleischer

  2. Department of Computer Science, The Hong Kong University of Science and Technology, Hong Kong

    Gerhard Trippen

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© 2004 Springer-Verlag Berlin Heidelberg

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Cai, JY., Watanabe, O. (2004). Random Access to Advice Strings and Collapsing Results. In: Fleischer, R., Trippen, G. (eds) Algorithms and Computation. ISAAC 2004. Lecture Notes in Computer Science, vol 3341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30551-4_20

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  • DOI: https://doi.org/10.1007/978-3-540-30551-4_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24131-7

  • Online ISBN: 978-3-540-30551-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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