Nawrotzki’s Algorithm for the Countable Splitting Lemma, Constructively ((Co)algebraic pearls)

Authors Ana Sokolova, Harald Woracek

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Author Details

Ana Sokolova
  • Department of Computer Sciences, University of Salzburg, Austria
Harald Woracek
  • Institute of Analysis and Scientific Computing, TU Wien, Austria


We are indebted to Paul Levy for bringing this topic to us by asking us several years ago to figure out some details of Nawrotzki’s algorithm, in particular its constructivity.

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Ana Sokolova and Harald Woracek. Nawrotzki’s Algorithm for the Countable Splitting Lemma, Constructively ((Co)algebraic pearls). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 23:1-23:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We reprove the countable splitting lemma by adapting Nawrotzki’s algorithm which produces a sequence that converges to a solution. Our algorithm combines Nawrotzki’s approach with taking finite cuts. It is constructive in the sense that each term of the iteratively built approximating sequence as well as the error between the approximants and the solution is computable with finitely many algebraic operations.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Mathematical analysis
  • Mathematics of computing → Probability and statistics
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Semantics and reasoning
  • countable splitting lemma
  • distributions with given marginals
  • couplings


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