Series-Parallel-Loop Decompositions of Control-flow Graphs

TL;DR

This paper introduces a new grammar-based decomposition framework for control-flow graphs that precisely characterizes structured program CFGs, leading to improved algorithms for compiler optimization tasks like register allocation and redundancy elimination.

Contribution

The paper presents a novel decomposition method that exactly captures structured program CFGs and enhances existing algorithms for compiler optimization.

Findings

Significant performance improvements over previous methods

Framework precisely characterizes CFGs of structured programs

Enhanced algorithms for register allocation and redundancy elimination

Abstract

Control-flow graphs (CFGs) of structured programs are well known to exhibit strong sparsity properties. Traditionally, this sparsity has been modeled using graph parameters such as treewidth and pathwidth, enabling the development of faster parameterized algorithms for tasks in compiler optimization, model checking, and program analysis. However, these parameters only approximate the structural constraints of CFGs: although every structured CFG has treewidth at most~7, many graphs with treewidth at most~7 cannot arise as CFGs. As a result, existing parameterized techniques are optimized for a substantially broader class of graphs than those encountered in practice. In this work, we introduce a new grammar-based decomposition framework that characterizes \emph{exactly} the class of control-flow graphs generated by structured programs. Our decomposition is intuitive, mirrors the syntactic structure of programs, and remains fully compatible with the dynamic-programming paradigm of treewidth-based methods. Using this framework, we design improved algorithms for two classical compiler optimization problems: \emph{Register Allocation} and \emph{Lifetime-Optimal Speculative Partial Redundancy Elimination (LOSPRE)}. Extensive experimental evaluation demonstrates significant performance improvements over previous state-of-the-art approaches, highlighting the benefits of using decompositions tailored specifically to CFGs.