arXiv subjects

Xuran Cai

Publications and source records attributed to Xuran Cai.

4 recordsLinked to original sources

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↗

arXiv2025

Enhancing Compiler Optimization Efficiency through Grammatical Decompositions of Control-Flow Graphs

This thesis addresses the complexities of compiler optimizations, such as register allocation and Lifetime-optimal Speculative Partial Redundancy Elimination (LOSPRE), which are often handled using tree decomposition algorithms. However, these methods frequently overlook important sparsity aspects of Control Flow Graphs (CFGs) and result in high computational costs. We introduce the SPL (Series-Parallel-Loop) decomposition, a novel framework that offers optimal solutions to these challenges. A key contribution is the formulation of a general solution for Partial Constraint Satisfaction Problems (PCSPs) within graph structures, applied to three optimization problems. First, SPL decomposition enhances register allocation by accurately modeling variable interference graphs, leading to efficient register assignments and improved performance across benchmarks. Second, it optimizes LOSPRE by effectively identifying and eliminating redundancies in program execution. Finally, the thesis focuses on optimizing the placement of bank selection instructions to enhance data retrieval efficiency and reduce latency. Extensive experimentation demonstrates significant performance improvements over existing methods, establishing SPL decomposition as a powerful tool for complex compiler optimizations, including register allocation, LOSPRE, and bank selection.

cs.PL↗

arXiv2025

Polynomial Invariant Generation for Floating-Point Programs

In numeric-intensive computations, it is well known that the execution of floating-point programs is imprecise as floating-point arithmetic incurs round-off errors. Although round-off errors are small for a single floating-point operation, the aggregation of such errors may be dramatic and cause catastrophic program failures. Therefore, to ensure the correctness of floating-point programs, round-off error needs to be carefully taken into account. In this work, we consider polynomial invariant generation for floating-point programs, aiming at generating tight invariants under the perturbation of round-off errors. Our contribution is a novel framework for applying polynomial constraint solving to address the invariant generation problem, which is also the first polynomial constraint solving based approach that handles floating-point errors to our best knowledge. In our framework, we propose a novel combination of round-off error analysis and polynomial constraint solving, aiming to circumvent the cost of handling a large number of error variables in the floating-point model. Experimental results over a variety of challenging benchmarks show that our framework outperforms SOTA approaches in both time efficiency and the precision of generated invariants.

cs.PL↗