The Hardness of Decision Tree Complexity

Authors Bruno Loff , Alexey Milovanov



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Author Details

Bruno Loff
  • LASIGE, Faculdade de Ciências, Universidade de Lisboa, Portugal
Alexey Milovanov
  • LASIGE, Faculdade de Ciências, Universidade de Lisboa, Portugal

Acknowledgements

The authors would like to thank Wei Zhan for his answer at StackOverflow.

Cite As Get BibTex

Bruno Loff and Alexey Milovanov. The Hardness of Decision Tree Complexity. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 66:1-66:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.STACS.2025.66

Abstract

Let f be a Boolean function given as either a truth table or a circuit. How difficult is it to find the decision tree complexity, also known as deterministic query complexity, of f in both cases? We prove that this problem is NC¹-hard and PSPACE-hard, respectively. The second bound is tight, and the first bound is close to being tight.

Subject Classification

ACM Subject Classification
  • Theory of computation
Keywords
  • Decision tree
  • Log-depth circuits

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