Author:
Kahn David M.,Hoffmann Jan
Abstract
AbstractAutomatic amortized resource analysis (AARA) is a type-based technique for inferring concrete (non-asymptotic) bounds on a program’s resource usage. Existing work on AARA has focused on bounds that are polynomial in the sizes of the inputs. This paper presents and extension of AARA to exponential bounds that preserves the benefits of the technique, such as compositionality and efficient type inference based on linear constraint solving. A key idea is the use of the Stirling numbers of the second kind as the basis of potential functions, which play the same role as the binomial coefficients in polynomial AARA. To formalize the similarities with the existing analyses, the paper presents a general methodology for AARA that is instantiated to the polynomial version, the exponential version, and a combined system with potential functions that are formed by products of Stirling numbers and binomial coefficients. The soundness of exponential AARA is proved with respect to an operational cost semantics and the analysis of representative example programs demonstrates the effectiveness of the new analysis.
Publisher
Springer International Publishing
Reference56 articles.
1. Albert, E., Arenas, P., Genaim, S., Puebla, G., Zanardini, D.: Cost Analysis of Java Bytecode. In: 16th Euro. Symp. on Prog. (ESOP’07) (2007)
2. Albert, E., Fernández, J.C., Román-Díez, G.: Non-cumulative Resource Analysis. In: Tools and Algorithms for the Construction and Analysis of Systems - 21st International Conference, (TACAS’15) (2015)
3. Albert, E., Genaim, S., Masud, A.N.: On the Inference of Resource Usage Upper and Lower Bounds. ACM Transactions on Computational Logic 14(3) (2013)
4. Atkey, R.: Amortised Resource Analysis with Separation Logic. In: 19th Euro. Symp. on Prog. (ESOP’10) (2010)
5. Avanzini, M., Lago, U.D., Moser, G.: Analysing the Complexity of Functional Programs: Higher-Order Meets First-Order. In: 29th Int. Conf. on Functional Programming (ICFP’15) (2012)
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