Combining Self-reducibility and Partial Information Algorithms

  • André Hernich
  • Arfst Nickelsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3618)


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.


Normal Form Polynomial Time Boolean Function Leaf Node Partial Information 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • André Hernich
    • 1
  • Arfst Nickelsen
    • 2
  1. 1.Humboldt-Universität zu BerlinGermany
  2. 2.Technische Universität BerlinGermany

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