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Analysis of Logarithmic Amortised Complexity [article]

Martin Hofmann, Georg Moser
2018 arXiv   pre-print
This type system gives rise to logarithmic and polynomial bounds on the runtime complexity and is the first such system to exhibit logarithmic amortised complexity.  ...  We relate the thus obtained automatable amortised resource analysis to manual amortised analyses of self-adjusting data structures, like splay trees, that can be found in the literature.  ...  The novelty of our contribution is that this is the first automatable approach to logarithmic amortised complexity.  ... 
arXiv:1807.08242v1 fatcat:y4kervru7vctjgjtgbjrfphzei

Type-based analysis of logarithmic amortised complexity

Martin Hofmann, Lorenz Leutgeb, David Obwaller, Georg Moser, Florian Zuleger
2021 Mathematical Structures in Computer Science  
The type system makes use of logarithmic potential functions and is the first such system to exhibit logarithmic amortised complexity.  ...  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 potentialbased.  ...  In future work, we aim at extension of the developed prototypes to a fully automated analysis of logarithmic amortised complexity.  ... 
doi:10.1017/s0960129521000232 fatcat:huihwcvu7vdvdgi2ue74qplpka

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

Lorenz Leutgeb, Georg Moser, Florian Zuleger
2021 Lecture Notes in Computer Science  
In this paper, we report on the first fully-automated amortised complexity analysis of self-adjusting data structures.  ...  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  ...  The methodology of amortised analysis allows one to assign a low (e.g., constant or logarithmic) amortised cost to a data structure operation even though the worst-case cost of a single operation might  ... 
doi:10.1007/978-3-030-81688-9_5 fatcat:edp7b45jyvaxve5kmaz3lci2h4

Automated Expected Amortised Cost Analysis of Probabilistic Data Structures [article]

Lorenz Leutgeb and Georg Moser and Florian Zuleger
2022 arXiv   pre-print
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  ...  The latter allows for the specification of fine-grained cost models.  ...  amortised complexity bound of 9 /8 log 2 (|t|) for splay is computed by our analysis.  ... 
arXiv:2206.03537v1 fatcat:d54bb47udzagfoszsrfyckhnrq

Automated amortised resource analysis for term rewrite systems

Georg Moser, Manuel Schneckenreither
2019 Science of Computer Programming  
Based on earlier work on amortised resource analysis, we establish a novel automated amortised resource analysis for term rewrite systems.  ...  The method is presented in an inference system akin to a type system and gives rise to polynomial bounds on the innermost runtime complexity of the analysed term rewrite system.  ...  Secondly, we aim to overcome the restriction to constant amortised analysis and provide an automated (or at least automatable) method establishing logarithmic amortised analysis.  ... 
doi:10.1016/j.scico.2019.102306 fatcat:emortgdhmzfejoxuztc545hywq

Automated Amortised Resource Analysis for Term Rewrite Systems [chapter]

Georg Moser, Manuel Schneckenreither
2018 Lecture Notes in Computer Science  
In this paper we establish an automated amortised resource analysis for term rewrite systems.  ...  This extends the provided analysis to a fully automated resource analysis of higher-order functional programs.  ...  Secondly, we aim to overcome the restriction to constant amortised analysis and provide an automated (or at least automatable) method establishing logarithmic amortised analysis.  ... 
doi:10.1007/978-3-319-90686-7_14 fatcat:bxr3h7kkovg67bcl4llybqmjju

Goodwill and accounting discretion

Marco Bisogno
2015 Scholedge International Journal of Management & Development ISSN 2394-3378  
</p><p>Design/methodology/approach: The study refers to a sample of Italian listed firms and the analysis covers three years, with a total of 591 firm-year observations.  ...  </p><p>Practical implications: Findings of the study could be relevant for standard-setters in future revisions of goodwill accounting.  ...  total debt / total assets; SIZE = natural logarithm of total assets; CF = operating cash flow; ROA = Return on Assets; ATA = natural logarithm of absolute value of total accruals. ***, **, *, Statistical  ... 
doi:10.19085/journal.sijmd021002 fatcat:6md2e6srjnc7bop2myenxrflce

Marked Ancestor Problems

Stephen Alstrup, Thore Husfeldt, Theis Rauhe
1998 BRICS Report Series  
<br /> [Extended abstract appears in Motwani, editor, 39th Annual Symposium on Foundations of Computer Science, FOCS '98 Proceedings, 1998, pages 534-543.]  ...  and even if we change to amortised analysis.  ...  The bound (1) holds for the worst case complexity of both the incremental and the decremental problem, as well as for the amortised complexity of the fully dynamic problem.  ... 
doi:10.7146/brics.v5i16.21956 fatcat:jiip2hzbnrgq7m3c3cspryetjy

Fully Dynamic Transitive Closure in plane dags with one source and one sink [chapter]

Thore Husfeldt
1995 Lecture Notes in Computer Science  
We also give a lower bound of Ω(log n/ log log n) on the amortised complexity of the problem in the cell probe model with logarithmic word size.  ...  for arbitrary vertices u and v can be answered in logarithmic time. The size of the data structure and the initialisation time are linear in the number of edges.  ...  Fredman and Saks give a lower bound of Ω(log n/ log log n) on the amortised complexity of the Dynamic Parity Prefix Problem: Given a vector x 1 , . . ., x n of bits, maintain a data structure that is able  ... 
doi:10.1007/3-540-60313-1_144 fatcat:c4comackdbgorgdspqbcamejry

Fully Dynamic Transitive Closure in Plane Dags with one Source and one Sink

Thore Husfeldt
1994 BRICS Report Series  
<br /> <br />We also give a lower bound of Omega(log n/log log n) on the amortised complexity of the problem in the cell probe model with logarithmic word size.  ...  for arbitrary vertices u and v can be answered in logarithmic time. The size of the data structure and the initialisation time are linear in the number of edges.  ...  Fredman and Saks give a lower bound of Ω(log n/ log log n) on the amortised complexity of the Dynamic Parity Prefix Problem: Given a vector x 1 , . . ., x n of bits, maintain a data structure that is able  ... 
doi:10.7146/brics.v1i30.21613 fatcat:ljwdxqn2azcivh2wsisrqvtypi

Improvements to a Resource Analysis for Hume [chapter]

Hans-Wolfgang Loidl, Steffen Jost
2010 Lecture Notes in Computer Science  
The core of our resource analysis for the embedded systems language Hume is a resource-generic, type-based inference engine that employs the concept of amortised costs to statically infer resource bounds  ...  Finally, we demonstrate improvements in the performance of our analysis.  ...  Amortised Costs: The concept of amortised costs has first been developed in the context of complexity analysis by Tarjan [27] .  ... 
doi:10.1007/978-3-642-15331-0_2 fatcat:c6c2wqfzbnem5otr74sjfpkp4a

What drives the allocation of the purchase price to goodwill?

Martin Bugeja, Anna Loyeung
2015 Journal of Contemporary Accounting and Economics  
The amount allocated to goodwill also increases after Australia adopted IFRS which no longer required goodwill to be systematically amortised.  ...  This study examines the proportion of the purchase price allocated to goodwill after the successful acquisition of a publicly listed firm.  ...  We then conduct an analysis of the factors which are associated with the proportion of the purchase price recorded as goodwill.  ... 
doi:10.1016/j.jcae.2015.10.002 fatcat:d7m6oi7eivfyhidrebomacun5a

Marked Ancestor Problems (Preliminary Version)

Stephen Alstrup, Thore Husfeldt, Theis Rauhe
1998 BRICS Report Series  
<br /> As easy corollaries we prove (often optimal) lower bounds on a number of problems.  ...  Our upper bounds improve a number of algorithms from various fields, including dynamic dictionary matching and coloured ancestor problems.  ...  and even if we change to amortised analysis.  ... 
doi:10.7146/brics.v5i7.19279 fatcat:5pkc3trj6ncrhad4urtk7skuyu

RLE Edit Distance in Near Optimal Time

Raphaël Clifford, Pawel Gawrychowski, Tomasz Kociumaka, Daniel P. Martin, Przemyslaw Uznanski, Michael Wagner
2019 International Symposium on Mathematical Foundations of Computer Science  
ACM Subject Classification Theory of computation → Design and analysis of algorithms; Theory of computation → Data structures design and analysis  ...  This improves the previous record by a factor of O(n/ log(mn)). The running time of our algorithm is within subpolynomial factors of being optimal, subject to the standard SETH-hardness assumption.  ...  Complexity Analysis We complete this section by showing that the aforementioned operations run in amortised logarithmic time. Lemma 7.  ... 
doi:10.4230/lipics.mfcs.2019.66 dblp:conf/mfcs/CliffordGKMU19 fatcat:pu6uwgwtkzfntlfm6jiq3lm3r4

The Value Relevance of Goodwill: IFRSs and Global Financial Crisis (GFC)

Ng Shir Li, Dennis W Taylor
2018 International Journal of Accounting and Financial Reporting  
The independent variables consist of earnings per share, book value per share, goodwill in the balance sheet, goodwill in the income statement (goodwill amortisation and goodwill impairment) and goodwill  ...  Also, the age of goodwill recorded in the balance sheet does not affect the value relevance of earnings and book value in the post-adoption period.  ...  Assumptions in Parametric Data Analysis Parametric data are required in regression analysis.  ... 
doi:10.5296/ijafr.v8i2.12830 fatcat:yfhhnwr2onarhgndz2gc2wyeh4
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