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arXiv · 2206.03537

Automated Expected Amortised Cost Analysis of Probabilistic Data Structures

Lorenz Leutgeb·Georg Moser·Florian Zuleger
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Abstract

In this paper, we present the first fully-automated expected amortised cost analysis of self-adjusting data structures, that is, of randomised splay trees, randomised splay heaps and randomised meldable heaps, which so far have only (semi-) manually been analysed in the literature. Our analysis is stated as a type-and-effect system for a first-order functional programming language with support for sampling over discrete distributions, non-deterministic choice and a ticking operator. The latter allows for the specification of fine-grained cost models. We state two soundness theorems based on two different -- but strongly related -- typing rules of ticking, which account differently for the cost of non-terminating computations. Finally we provide a prototype implementation able to fully automatically analyse the aforementioned case studies.

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Lorenz Leutgeb, Georg Moser, Florian Zuleger. 2022-06-07. Automated Expected Amortised Cost Analysis of Probabilistic Data Structures. https://doi.org/10.1007/978-3-031-13188-2_4

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