可变性维护可约流程图中的循环嵌套森林
Fully Dynamic Maintenance of Loop Nesting Forests in Reducible Flow Graphs
AI总结：
本文提出首个动态算法维护可约控制流图中的循环嵌套森林，利用动态DFS维护技术实现边插入删除下的增量更新，避免全局重计算，提升编译器分析效率。
摘要：
循环嵌套森林（LNFs）是分析控制流结构的基本抽象，应用于编译器优化、程序分析和支配计算。尽管静态构建LNFs的高效算法已为人所知，但在动态图更新下维护仍鲜有研究，因缺乏高效的动态深度优先搜索（DFS）维护方法。本文首次提出维护可约控制流图中循环嵌套森林的完全动态算法。我们的方法利用动态DFS维护的最新进展，实现边插入和删除下的循环结构增量更新。我们证明更新可限制在深度优先生成树的局部区域，避免全局重计算。我们提供了形式不变量、正确性论证和复杂度分析，并展示了维护的LNF如何高效推导支配信息。我们的结果确立LNFs作为现代编译器和分析流水线的实用动态抽象。
英文摘要：
Loop nesting forests (LNFs) are a fundamental abstraction for reasoning about control-flow structure, enabling applications such as compiler optimizations, program analysis, and dominator computation. While efficient static algorithms for constructing LNFs are well understood, maintaining them under dynamic graph updates has remained largely unexplored due to the lack of efficient dynamic depth-first search (DFS) maintenance. In this paper, we present the first fully dynamic algorithm for maintaining loop nesting forests in reducible control-flow graphs. Our approach leverages recent advances in dynamic DFS maintenance to incrementally update loop structure under edge insertions and deletions. We show that updates can be confined to local regions of the depth-first spanning tree, avoiding global recomputation. We provide formal invariants, correctness arguments, and complexity analysis, and demonstrate how the maintained LNF enables efficient derivation of dominance information. Our results establish LNFs as a practical dynamic abstraction for modern compiler and analysis pipelines.
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