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Combining Self-reducibility and Partial Information Algorithms

  • Conference paper
Mathematical Foundations of Computer Science 2005 (MFCS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3618))

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Abstract

A partial information algorithm for a language A computes, for some fixed m, for input words x 1, ..., x m a set of bitstrings containing χ A (x 1,...,x m ). E.g., p-selective, approximable, and easily countable languages are defined by the existence of polynomial-time partial information algorithms of specific type. Self-reducible languages, for different types of self-reductions, form subclasses of PSPACE.

For a self-reducible language A, the existence of a partial information algorithm sometimes helps to place A into some subclass of PSPACE. The most prominent known result in this respect is: P-selective languages which are self-reducible are in P [9].

Closely related is the fact that the existence of a partial information algorithm for A simplifies the type of reductions or self-reductions to A. The most prominent known result in this respect is: Turing reductions to easily countable languages simplify to truth-table reductions[8].

We prove new results of this type. We show:

  1. 1

    Self-reducible languages which are easily 2-countable are in P. This partially confirms a conjecture of [8].

  2. 2

    Self-reducible languages which are (2m – 1,m)-verbose are truth-table self-reducible. This generalizes the result of [9] for p-selective languages, which are (m + 1,m)-verbose.

  3. 3

    Self-reducible languages, where the language and its complement are strongly 2-membership comparable, are in P. This generalizes the corresponding result for p-selective languages of [9].

  4. 4

    Disjunctively truth-table self-reducible languages which are 2-membership comparable are in UP.

Topic: Structural complexity.

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Authors and Affiliations

  1. Humboldt-Universität zu Berlin, Germany

    André Hernich

  2. Technische Universität Berlin, Germany

    Arfst Nickelsen

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  1. André Hernich
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  2. Arfst Nickelsen
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Editors and Affiliations

  1. Institute of Mathematics, Gdansk University, Wita Stwosza 57, 80 952, Gdansk, Poland

    Joanna Jȩdrzejowicz  & Andrzej Szepietowski  & 

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Hernich, A., Nickelsen, A. (2005). Combining Self-reducibility and Partial Information Algorithms. In: Jȩdrzejowicz, J., Szepietowski, A. (eds) Mathematical Foundations of Computer Science 2005. MFCS 2005. Lecture Notes in Computer Science, vol 3618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11549345_42

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  • DOI: https://doi.org/10.1007/11549345_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28702-5

  • Online ISBN: 978-3-540-31867-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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