Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination of programs operating on integers. To this end, a variety of acceleration techniques has been proposed. However, all of them are monolithic: Either they accelerate a loop successfully or they fail completely. In contrast, we present a calculus that allows for combining acceleration techniques in a modular way and we show how to integrate many existing acceleration techniques into our calculus. Moreover, we propose two novel acceleration techniques that can be incorporated into our calculus seamlessly. An empirical evaluation demonstrates the applicability of our approach.

中文翻译：

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模块化环路加速的微积分

循环加速可用于证明对整数操作的程序的安全性、可达性、运行时界限和（非）终止。为此，提出了多种加速技术。然而，它们都是整体的：要么成功加速循环，要么完全失败。相比之下，我们提出了一种允许以模块化方式组合加速技术的微积分，并展示了如何将许多现有的加速技术集成到我们的微积分中。此外，我们提出了两种新颖的加速技术，可以无缝地融入我们的微积分中。实证评估证明了我们方法的适用性。