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A constructive generalization of the borel-cantelli lemma with application to the complexity of infinite strings

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Abstract

This paper concerns a constructive adaptation of the classical Borel-Cantelli lemma which allows us to solve such decomposition problems as: when does there exist an infinite object that is decomposable into infinitely many parts that are maximally complex? A constructive proof is supplied of the key theorem and its degree is characterized. For completeness a classical (i.e., nonconstructive) proof is also provided.

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Authors and Affiliations

  1. School of Information and Computer Science, Georgia Institute of Technology, 30332, Atlanta, Georgia, USA

    Richard A. DeMillo

  2. Department of Computer Science, Yale University, 06520, New Haven, Connecticut, USA

    Richard J. Lipton

Authors
  1. Richard A. DeMillo
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  2. Richard J. Lipton
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Additional information

This research was supported in part by NSF Grants MCS78-81486 and MCS77-28305, and was also facilitated by the use of Theory Net, NSF Grant No. MCS78-01689.

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DeMillo, R.A., Lipton, R.J. A constructive generalization of the borel-cantelli lemma with application to the complexity of infinite strings. Math. Systems Theory 13, 95–104 (1979). https://doi.org/10.1007/BF01744291

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  • DOI: https://doi.org/10.1007/BF01744291

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