Amir Goharshady | Searcharxiv

arXiv2026

Series-Parallel-Loop Decompositions of Control-flow Graphs

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.

cs.PL↗

arXiv2026

Efficient Algorithms for Partial Constraint Satisfaction Problems over Control-flow Graphs

In this work, we focus on the Partial Constraint Satisfaction Problem (PCSP) over control-flow graphs (CFGs) of programs. PCSP serves as a generalization of the well-known Constraint Satisfaction Problem (CSP). In the CSP framework, we define a set of variables, a set of constraints, and a finite domain $D$ that encompasses all possible values for each variable. The objective is to assign a value to each variable in such a way that all constraints are satisfied. In the graph variant of CSP, an underlying graph is considered and we have one variable corresponding to each vertex of the graph and one or several constraints corresponding to each edge. In PCSPs, we allow for certain constraints to be violated at a specified cost, aiming to find a solution that minimizes the total cost. Numerous classical compiler optimization tasks can be framed as PCSPs over control-flow graphs. Examples include Register Allocation, Lifetime-optimal Speculative Partial Redundancy Elimination (LOSPRE), and Optimal Placement of Bank Selection Instructions. On the other hand, it is well-known that control-flow graphs of structured programs are sparse and decomposable in a variety of ways. In this work, we rely on the Series-Parallel-Loop (SPL) decompositions as introduced by~\cite{RegisterAllocation}. Our main contribution is a general algorithm for PCSPs over SPL graphs with a time complexity of $O(|G| \cdot |D|^6)$, where $|G|$ represents the size of the control-flow graph. Note that for any fixed domain $D,$ this yields a linear-time solution. Our algorithm can be seen as a generalization and unification of previous SPL-based approaches for register allocation and LOSPRE. In addition, we provide experimental results over another classical PCSP task, i.e. Optimal Bank Selection, achieving runtimes four times better than the previous state of the art.

cs.CL↗