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The complexity of generating test instances

  • Complexity Theory II
  • Conference paper
  • First Online:
STACS 97 (STACS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1200))

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Abstract

Recently, Osamu Watanabe proposed a new framework for testing the correctness and average case behavior of algorithms that purport to solve a given NP search problem efficiently on average. The idea is to randomly generate certified instances in a way that resembles the underlying distribution μ. We discuss this approach and show that test instances can be generated for every NP search problem with non-adaptive queries to an NP oracle. Further, we introduce Las Vegas as well as Monte Carlo types of test instance generators. We show that these generators can be used to find out whether an algorithm is correct and efficient on average under μ. In fact, it is not hard to construct Monte Carlo generators for all RP search problems as well as Las Vegas generators for all ZPP search problems. On the other hand, we prove that (under the uniform distribution) Monte Carlo generators can only exist for problems in NP ∩ co-AM.

Supported by the Deutsche Forschungsgemeinschaft, research grant Schö 302/4-2.

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Authors and Affiliations

  1. Abteilung Theoretische Informatik, Universität Ulm, 89069, Ulm, Germany

    Christoph Karg, Johannes Köbler & Rainer Schuler

Authors
  1. Christoph Karg
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  2. Johannes Köbler
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  3. Rainer Schuler
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Editor information

Rüdiger Reischuk Michel Morvan

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© 1997 Springer-Verlag Berlin Heidelberg

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Karg, C., Köbler, J., Schuler, R. (1997). The complexity of generating test instances. In: Reischuk, R., Morvan, M. (eds) STACS 97. STACS 1997. Lecture Notes in Computer Science, vol 1200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023474

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  • DOI: https://doi.org/10.1007/BFb0023474

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62616-9

  • Online ISBN: 978-3-540-68342-1

  • eBook Packages: Springer Book Archive

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