Verified Analysis of Random Binary Tree Structures

Manuel Eberl, Max W. Haslbeck, Tobias Nipkow

Journal of Automated Reasoning 64, pp. 879 – 910, 2020.


This work is a case study of the formal verification and complexity ana- lysis of some famous probabilistic algorithms and data structures in the proof assistant Isabelle/HOL. In particular, we consider the expected number of comparisons in ran- domised quicksort, the relationship between randomised quicksort and average-case deterministic quicksort, the expected shape of an unbalanced random Binary Search Tree, the randomised binary search trees described by Martínez and Roura, and the expected shape of a randomised treap. The last three have, to our knowledge, not been analysed using a theorem prover before and the last one is of particular interest because it involves continuous distributions.


  PDF |    doi:10.1007/s10817-020-09545-0


author = "Manuel Eberl and Max W. Haslbeck and Tobias Nipkow",
title = "Verified Analysis of Random Binary Tree Structures",
series = "J Autom Reasoning",
volume = 64,
pages = "879--910",
year = 2020,
doi = "10.1007/s10817-020-09545-0"
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