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Computing Periods\(\ldots \)

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WALCOM: Algorithms and Computation (WALCOM 2018)

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Abstract

A period is the difference between the volumes of two semi-algebraic sets. Recent research has located their worst-case complexity in low levels of the Grzegorczyk Hierarchy. The present work introduces, analyzes, and evaluates three rigorous algorithms for rigorously computing periods: a deterministic, a randomized, and a ‘transcendental’ one.

Based on ideas presented at CCA 2017, this work was supported by the National Research Foundation of Korea (grant NRF-2017R1E1A1A03071032) and the International Research & Development Program of the Korean Ministry of Science and ICT (grant NRF-2016K1A3A7A03950702). We thank the anonymous referees for feedback!

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Notes

  1. 1.

    Of course the specific periods \(\pi \) and \(\ln (2)\) admit other, more efficient algorithms.

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Authors and Affiliations

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

    Junhee Cho, Sewon Park & Martin Ziegler

Authors
  1. Junhee Cho
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  2. Sewon Park
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  3. Martin Ziegler
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Correspondence to Junhee Cho .

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Editors and Affiliations

  1. Bangladesh University of Engineering and Technology, Dhaka, Bangladesh

    M. Sohel Rahman

  2. National University of Singapore , Singapore, Singapore

    Wing-Kin Sung

  3. Japan Advanced Institute of Science and Technology, Ishikawa, Japan

    Ryuhei Uehara

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Cho, J., Park, S., Ziegler, M. (2018). Computing Periods\(\ldots \) . In: Rahman, M., Sung, WK., Uehara, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2018. Lecture Notes in Computer Science(), vol 10755. Springer, Cham. https://doi.org/10.1007/978-3-319-75172-6_12

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  • DOI: https://doi.org/10.1007/978-3-319-75172-6_12

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  • Online ISBN: 978-3-319-75172-6

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