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P2 Inferring Complexity Bounds from Recurrence Relations

从递推关系推断复杂度界
FSE Proceedings of the 31st ACM Joint European Software Engineering Conference and Symposium on the Foundations of Software Engineering2023匹配度 3/10 · 论文属于程序分析与复杂度界推断,但与用户核心关注的静态分析+LLM/Agent、浮点程序分析、贝叶斯程序分析等方向没有直接交集;其动态推断递推关系的方法也不是用户强调的静态分析或AI辅助形式化验证。引用 0 inbox
Didier Ishimwe
crossref: 2026-09-12dblp: 2026-09-12

AI 速览

一句话:提出从执行轨迹动态推断递推关系并求解,为非确定性递归程序计算渐近复杂度界。

本文关注如何自动确定非确定性递归程序的渐近复杂度界。作者提出从程序执行轨迹中动态推断递推关系,再使用 annihilator method 和 Master Theorem 求解递推,得到表示复杂度界的闭式解。初步评估在若干经典递归程序上进行:方法能学到正确界,如 quicksort 的 O(n²);对指数程序给出比已有结果更精确的界,如 Fibonacci;并可捕获非线性多项式、非多项式、对数及指数等多种复杂度关系。

问题
如何自动推断非确定性递归程序的渐近复杂度界。
方法
从程序执行轨迹动态推断递推关系,并结合 annihilator method 与 Master Theorem 求解闭式解。
评估
在经典递归程序上进行初步评估,能够学到 quicksort 的 O(n²) 等正确界,并为 Fibonacci 等指数程序给出更精确的界,覆盖多种复杂度关系。
原文摘要(Abstract)

Determining program complexity bounds is a fundamental problem with a variety of applications in software development. In this paper we present a novel approach for computing the asymptotic complexity bounds of non-deterministic recursive programs by solving dynamically inferred recurrence relations. Recurrences are inferred from program execution traces and solved using the annihilator method and Master Theorem to obtain closed-form solutions representing the complexity bounds. Our preliminary evaluation shows that this approach can learn correct bounds for popular classical recursive programs (e.g. O(n2) for quicksort), achieving more precise bounds for exponential programs than previously reported (e.g. O((1+√5/2)n) for fibonacci), and capturing a wide range of bounds including non-linear polynomial and non-polynomial, logarithmic, and exponential relations.

链接与引用

DOI 原文 · PDF(开放获取) · DBLP

BibTeX
@inproceedings{Ishimwe23,
  title = {Inferring Complexity Bounds from Recurrence Relations},
  author = {Didier Ishimwe},
  booktitle = {FSE},
  year = {2023},
  doi = {10.1145/3611643.3617853}
}