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Certified Computation of Nondeterministic Limits

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Book cover NASA Formal Methods (NFM 2022)

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Abstract

The computational content of constructive metric completeness is the operator that computes limits of Cauchy sequences. It can be used to construct certified programs that compute interesting transcendental real numbers from sequences of approximations. The desired nondeterministic version of it would be to nondeterministically compute real numbers from nondeterministic approximations. However, it is not obvious how nondeterministic metric completeness should be formalized.

We extend previous work on the formalization of exact real computation by primitive properties of nondeterminism. We show that by these properties, various forms of nondeterministic metric completeness can be derived without extending the axiomatic structure of constructive real numbers. We further implement our theory in the Coq proof assistant and use Coq’s code extraction features to extract efficient exact real computation programs using several forms of nondeterministic computation.

Holger Thies is supported by JSPS KAKENHI Grant Number JP20K19744. Sewon Park is supported by JSPS KAKENHI Grant number JP18H03203. This project has received funding from the EU’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 731143. The authors thank Franz Brauße and Norbert Müller for helpful discussions.

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Notes

  1. 1.

    in the sense of computable analysis [30].

  2. 2.

    Nondeterministic functions are also known as multivalued functions.

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Authors and Affiliations

  1. Aston University, Birmingham, UK

    Michal Konečný

  2. Kyoto University, Kyoto, Japan

    Sewon Park & Holger Thies

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  1. Michal Konečný
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  2. Sewon Park
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  3. Holger Thies
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Correspondence to Holger Thies .

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Editors and Affiliations

  1. University of Southern California, Los Angeles, CA, USA

    Jyotirmoy V. Deshmukh

  2. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA

    Klaus Havelund

  3. National Institute of Aerospace, Hampton, VA, USA

    Ivan Perez

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Konečný, M., Park, S., Thies, H. (2022). Certified Computation of Nondeterministic Limits. In: Deshmukh, J.V., Havelund, K., Perez, I. (eds) NASA Formal Methods. NFM 2022. Lecture Notes in Computer Science, vol 13260. Springer, Cham. https://doi.org/10.1007/978-3-031-06773-0_41

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  • DOI: https://doi.org/10.1007/978-3-031-06773-0_41

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