Synchronous linear constraint system games

Adina Goldberg

doi:10.1063/5.0025647

Coderivatives and the Solution Map of a Linear Constraint System

SIAM Journal on Optimization ◽

10.1137/140998469 ◽

2016 ◽

Vol 26 (2) ◽

pp. 986-1007 ◽

Cited By ~ 8

Author(s):

Duong Thi Kim Huyen ◽

Nguyen Dong Yen

Keyword(s):

Linear Constraint ◽

Solution Map ◽

Constraint System

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ATLAS: Automated Amortised Complexity Analysis of Self-adjusting Data Structures

Computer Aided Verification - Lecture Notes in Computer Science ◽

10.1007/978-3-030-81688-9_5 ◽

2021 ◽

pp. 99-122

Author(s):

Lorenz Leutgeb ◽

Georg Moser ◽

Florian Zuleger

Keyword(s):

Potential Function ◽

Data Structures ◽

Recent Progress ◽

Complexity Analysis ◽

Target Function ◽

Linear Constraint ◽

Potential Functions ◽

Resource Analysis ◽

Constraint System ◽

Scalable Analysis

AbstractBeing able to argue about the performance of self-adjusting data structures such as splay trees has been a main objective, when Sleator and Tarjan introduced the notion of amortised complexity.Analysing these data structures requires sophisticated potential functions, which typically contain logarithmic expressions. Possibly for these reasons, and despite the recent progress in automated resource analysis, they have so far eluded automation. In this paper, we report on the first fully-automated amortised complexity analysis of self-adjusting data structures. Following earlier work, our analysis is based on potential function templates with unknown coefficients.We make the following contributions: 1) We encode the search for concrete potential function coefficients as an optimisation problem over a suitable constraint system. Our target function steers the search towards coefficients that minimise the inferred amortised complexity. 2) Automation is achieved by using a linear constraint system in conjunction with suitable lemmata schemes that encapsulate the required non-linear facts about the logarithm. We discuss our choices that achieve a scalable analysis. 3) We present our tool $$\mathsf {ATLAS}$$ ATLAS and report on experimental results for splay trees, splay heaps and pairing heaps. We completely automatically infer complexity estimates that match previous results (obtained by sophisticated pen-and-paper proofs), and in some cases even infer better complexity estimates than previously published.

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