Verified Analysis of Random Binary Tree Structures (extended journal version)

by Manuel Eberl, Max W. Haslbeck, and Tobias Nipkow

In: J. Autom. Reasoning (2020)

DOI:

Abstract:

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 Roura and Martinez, 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.

Note:

This is a revised and extended version of a 2018 ITP paper.

Download preprint PDF (549 KiB)

@article{eberl20jar,
  author="Eberl, Manuel and Haslbeck, Max W. and Nipkow, Tobias",
  title="Verified Analysis of Random Binary Tree Structures",
  journal="J. Autom. Reasoning",
  year="2020",
  month="feb",
  day="08",
  doi="10.1007/s10817-020-09545-0",
  issn="1573-0670"
}

Download BibTeX (282 Bytes)

(The final publication is available at link.springer.com)