Verified Analysis of Random Binary Tree Structures

Manuel Eberl, Max W. Haslbeck, Tobias Nipkow

This work is a case study of the formal verification and complexity analysis of some famous probabilistic algorithms and data structures in the proof assistant Isabelle/HOL. In particular, we consider the expected number of comparisons in randomised quicksort, the relationship between randomised quicksort and average-case deterministic quicksort, the expected shape of an unbalanced random Binary Search Tree, and the expected shape of a Treap. The last two 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.

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BibTeX:

@inproceedings{EberlHN-ITP18,
author={Manuel Eberl, Max W. Haslbeck, Tobias Nipkow},
title={Verified Analysis of Random Binary Tree Structures},
booktitle={Interactive Theorem Proving (ITP 2018)},
editor={J. Avigad and A. Mahboubi},
publisher=Springer,series=LNCS,volume={},pages={},year=2018}

Isabelle theories