Verified Analysis of Random Binary Tree Structures

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 qui...

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Bibliographic Details
Published in:Journal of automated reasoning Vol. 64; no. 5; pp. 879 - 910
Main Authors: Eberl, Manuel, Haslbeck, Max W., Nipkow, Tobias
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.06.2020
Springer Nature B.V
Subjects:
Algorithms
Artificial Intelligence
Binary system
Computer Science
Data structures
Mathematical Logic and Formal Languages
Mathematical Logic and Foundations
Randomization
Symbolic and Algebraic Manipulation
Theorem proving
Randomised algorithms
Binary search trees
Quicksort
Interactive theorem proving
Isabelle
Randomised data structures
ISSN:0168-7433, 1573-0670
Online Access:Get full text
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Summary: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.
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ISSN:0168-7433
1573-0670
DOI:10.1007/s10817-020-09545-0