Closure of Polynomial Time Partial Information Classes under Polynomial Time Reductions

  • Arfst Nickelsen
  • Till Tantau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2138)

Abstract

Polynomial time partial information classes are extensions of the class P of languages decidable in polynomial time. A partial information algorithm for a language A computes, for fixed n ∈ ℕ, on input of words x1,...,xn a set P of bitstrings, called a pool, such that χA(x1,...,xn) ∈ P, where P is chosen from a family \( \mathcal{D} \) of pools. A language A is in \( P\left[ \mathcal{D} \right] \), if there is a polynomial time partial information algorithm which for all inputs (x1,... xn) outputs a pool \( \mathcal{P} \in \mathcal{D} \) with χa(x1,..., xn) ∈ P. Many extensions of P studied in the literature, including approximable languages, cheatability, p-selectivity and frequency computations, form a class \( P\left[ \mathcal{D} \right] \) for an appropriate family \( \mathcal{D} \).

We characterise those families \( \mathcal{D} \) for which \( P\left[ \mathcal{D} \right] \) is closed under certain polynomial time reductions, namely bounded truth-table, truth-table, and Turing reductions. We also treat positive reductions. A class \( P\left[ \mathcal{D} \right] \) is presented which strictly contains the class P-sel of p-selective languages and is closed under positive truth-table reductions.

Keywords

structural complexity partial information polynomial time reductions verboseness p-selectivity positive reductions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Arfst Nickelsen
    • 1
  • Till Tantau
    • 1
  1. 1.Fakultät für Elektrotechnik und InformatikTechnische Universität BerlinBerlinGermany

Personalised recommendations