Automatic 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.

中文翻译：

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指数自动摊销资源分析

自动摊销资源分析 (AARA) 是一种基于类型的技术，用于推断程序资源使用的具体（非渐近）界限。AARA 的现有工作集中在输入大小的多项式边界上。本文介绍了 AARA 并将其扩展到指数边界，该边界保留了该技术的优点，例如基于线性约束求解的组合性和有效类型推断。一个关键思想是使用第二类斯特林数作为势函数的基础，其作用与多项式 AARA 中的二项式系数相同。为了形式化与现有分析的相似性，本文提出了 AARA 的一般方法，该方法被实例化为多项式版本，指数版本，以及具有由斯特林数和二项式系数的乘积形成的势函数的组合系统。指数 AARA 的可靠性在运营成本语义方面得到了证明，对代表性示例程序的分析证明了新分析的有效性。