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Software Testing in Computable Analysis

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Unconventional Computation and Natural Computation (UCNC 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14776))

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Abstract

We initiate research on software testing in the realm of computable analysis over the real numbers and general topological spaces. The goal is to develop a general framework and to show some first results of testing algorithms for checking probabilistically whether a Type-2 machine approximately performs the task it is supposed to. We give a testing algorithm for Type-2 programs supposed to compute the exponential function. As main result, we design a test whether a program approximately computes a univariate polynomial of given degree. Its analysis reveals close relations to computational learning theory.

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Notes

  1. 1.

    The use and meaning of parameters in [1] is slightly different from ours. The parameters \(\eta , \epsilon , \delta \) in [1] correspond to our \(\delta , \epsilon , \beta \), respectively.

  2. 2.

    Note that a dependence of \(m_0\) on \(\delta \) or \(Bdim(\delta )\), respectively, is hidden by the fact that \(Bdim(\delta )\) in our specific situation is bounded from above by \(15(d+1)\) and from below by \(d+1\), see Propositions 3.1 and 6.1 in [1].

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Acknowledgment

Thanks go to the anonymous referees for careful reading and several helpful remarks.

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Authors and Affiliations

  1. BTU Cottbus-Senftenberg, 03046, Cottbus, Germany

    Klaus Meer

  2. KAIST School of Computing, Daejeon, Republic of Korea

    Martin Ziegler

Authors
  1. Klaus Meer
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  2. Martin Ziegler
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Correspondence to Klaus Meer .

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Editors and Affiliations

  1. Ajou University, Suwon, Korea (Republic of)

    Da-Jung Cho

  2. Pohang University of Science and Technology, Pohang, Korea (Republic of)

    Jongmin Kim

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Meer, K., Ziegler, M. (2024). Software Testing in Computable Analysis. In: Cho, DJ., Kim, J. (eds) Unconventional Computation and Natural Computation. UCNC 2024. Lecture Notes in Computer Science, vol 14776. Springer, Cham. https://doi.org/10.1007/978-3-031-63742-1_5

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  • DOI: https://doi.org/10.1007/978-3-031-63742-1_5

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-031-63742-1

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