arXiv subjects

Berry Schoenmakers

Publications and source records attributed to Berry Schoenmakers.

6 recordsLinked to original sources

arXiv2026

Automated Amortised Analysis of Skew Heaps and Leftist Heaps (Extended Version)

We study the fully automated amortised analysis of purely functional data structures like skew heaps, as well as weight- and rank-biased leftist heaps. For that we generalise earlier works on automated amortised resource analysis by developing a type inference based approach with a generic type system. This allows for modular reasoning and the inference of precise and optimal cost bounds. More specifically, we extend the work on the ATLAS system by Leutgeb et al. which was developed to cover the analysis of splay trees and some closely related data structures. To enable the analysis of skew heaps, however, and the even more challenging (amortised) analysis of leftist heaps, we have developed a range of new techniques for type-based automated analysis. By introducing a generic type system we allow for arbitrary (classes of) potential functions, compared to the use of hard-coded potential functions in ATLAS, which we have implemented in Haskell in an entirely modular way. We have also greatly enhanced the existing type inference algorithm by extensions in multiple directions, including path-sensitive reasoning, data structure invariants, and template parameters for piecewise defined potential functions. We show how our newly developed system supports the use of all known potential functions for analysing skew heaps and leftist heaps, confirming the known bounds.

cs.PL↗

arXiv2024

Amortized Analysis of Leftist Heaps

Leftist heaps and skew heaps are two well-known data structures for mergeable priority queues. Leftist heaps are constructed for efficiency in the worst-case sense whereas skew heaps are self-adjusting, designed for efficiency in the amortized sense. In this paper, we analyze the amortized complexity of leftist heaps to initiate a full performance comparison with skew heaps. We consider both the leftist heaps originally developed by Crane and Knuth, which are also referred to as rank-biased (or, height-biased) leftist heaps, and the weight-biased leftist heaps introduced by Cho and Sahni. We show how weight-biased leftist heaps satisfy the same exact amortized bounds as skew heaps. With these matching bounds we establish a nice trade-off in which storage of weights is used to limit the worst-case complexity of leftist heaps, without affecting the amortized complexity compared to skew heaps. For rank-biased leftist heaps, we obtain the same amortized lower bounds as for skew heaps, but whether these bounds are tight is left as an open problem.

cs.DS↗

arXiv2018

Binary Pebbling Algorithms for In-Place Reversal of One-Way Hash Chains

We present optimal binary pebbling algorithms for in-place reversal (backward traversal) of one-way hash chains. For a hash chain of length $2^k$, the number of hashes performed in each output round does not exceed $\lceil k/2 \rceil$, whereas the number of hash values stored (pebbles) throughout is at most $k$. We introduce a framework for rigorous comparison of explicit binary pebbling algorithms, including simple speed-1 binary pebbling, Jakobsson's speed-2 binary pebbling, and our optimal binary pebbling algorithm. Explicit schedules describe for each pebble exactly how many hashes need to be performed in each round. The optimal schedule turns out to be essentially unique and exhibits a nice recursive structure, which allows for fully optimized implementations that can readily be deployed. In particular, we develop the first in-place implementations with minimal storage overhead (essentially, storing only hash values), and fast implementations with minimal computational overhead.

cs.CR↗

arXiv2007

Smooth Rényi Entropy of Ergodic Quantum Information Sources

We prove that the average smooth Renyi entropy rate will approach the entropy rate of a stationary, ergodic information source, which is equal to the Shannon entropy rate for a classical information source and the von Neumann entropy rate for a quantum information source.

quant-ph↗

arXiv2005

Generic Security Proof of Quantum Key Exchange using Squeezed States

Recently, a Quantum Key Exchange protocol that uses squeezed states was presented by Gottesman and Preskill. In this paper we give a generic security proof for this protocol. The method used for this generic security proof is based on recent work by Christiandl, Renner and Ekert.

quant-ph↗

arXiv2005

Quantum Information Theoretical Analysis of Various Constructions for Quantum Secret Sharing

Recently, an information theoretical model for Quantum Secret Sharing (QSS) schemes was introduced. By using this model, we prove that pure state Quantum Threshold Schemes (QTS) can be constructed from quantum MDS codes and vice versa. In particular, we consider stabilizer codes and give a constructive proof of their relation with QTS. Furthermore, we reformulate the Monotone Span Program (MSP) construction according to the information theoretical model and check the recoverability and secrecy requirement. Finally, we consider QSS schemes which are based on quantum teleportation.

quant-ph↗