{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/type-based-analysis-of-logarithmic-amortised","title":"Type-Based Analysis of Logarithmic Amortised Complexity","arxiv_id":"2101.12029","date":"2021-01-28","proceeding":null,"authors":["Martin Hofmann","Lorenz Leutgeb","Georg Moser","David Obwaller","Florian Zuleger"],"abstract":"We introduce a novel amortised resource analysis couched in a type-and-effect system. Our analysis is formulated in terms of the physicist's method of amortised analysis, and is potential-based. The type system makes use of logarithmic potential functions and is the first such system to exhibit *logarithmic amortised complexity*. With our approach we target the automated analysis of self-adjusting data structures, like splay trees, which so far have only manually been analysed in the literature. In particular, we have implemented a semi-automated prototype, which successfully analyses the zig-zig case of *splaying*, once the type annotations are fixed.","url_abs":"https://arxiv.org/abs/2101.12029v2","url_pdf":"https://arxiv.org/pdf/2101.12029v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"type-based-analysis-of-logarithmic-amortised","repo_url":"https://github.com/lorenzleutgeb/atlas","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"type-based-analysis-of-logarithmic-amortised","repo_url":"https://github.com/lorenzleutgeb/lac","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"type-based-analysis-of-logarithmic-amortised","repo_url":"https://github.com/lorenzleutgeb/logs","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}