Mathematical systems theory

, Volume 13, Issue 1, pp 95–104 | Cite as

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

  • Richard A. DeMillo
  • Richard J. Lipton


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.


Computational Mathematic Constructive Proof Decomposition Problem Constructive Adaptation Constructive Generalization 


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Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • Richard A. DeMillo
    • 1
  • Richard J. Lipton
    • 2
  1. 1.School of Information and Computer ScienceGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of Computer ScienceYale UniversityNew HavenUSA

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