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, 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.

中文翻译：

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随机二叉树结构的验证分析

这项工作是在证明助手 Isabelle/HOL 中对一些著名的概率算法和数据结构进行形式验证和复杂性分析的案例研究。特别地，我们考虑了随机快速排序中的预期比较次数、随机快速排序和平均情况确定性快速排序之间的关系、不平衡随机二叉搜索树的预期形状、Martínez 和 Roura 描述的随机二叉搜索树，以及随机收获的预期形状。据我们所知，最后三个之前没有使用定理证明器进行过分析，最后一个特别有趣，因为它涉及连续分布。