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Real Benefit of Promises and Advice

  • Klaus Ambos-Spies
  • Ulrike Brandt
  • Martin Ziegler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7921)

Abstract

Promises are a standard way to formalize partial algorithms; and advice quantifies nonuniformity. For decision problems, the latter is captured in common complexity classes such as \(\mathcal{P}/\operatorname{poly}\), that is, with advice growing in size with that of the input. We advertise constant-size advice and explore its theoretical impact on the complexity of classification problems – a natural generalization of promise problems – and on real functions and operators. Specifically we exhibit problems that, without any advice, are decidable/computable but of high complexity while, with (each increase in the permitted size of) advice, (gradually) drop down to polynomial-time.

Keywords

Turing Machine Multivalued Mapping Hard Core Kolmogorov Complexity Circuit Family 
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 2013

Authors and Affiliations

  • Klaus Ambos-Spies
    • 1
  • Ulrike Brandt
    • 2
  • Martin Ziegler
    • 3
  1. 1.Department of Mathematics and Computer ScienceRuprecht-Karls-Universität HeidelbergHeidelbergGermany
  2. 2.Department of Computer ScienceTechnische Universität DarmstadtDarmstadtGermany
  3. 3.Department of MathematicsTechnische Universität DarmstadtDarmstadtGermany

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