Constraint-solving-based program invariant synthesis takes a parametric invariant template and encodes the (inductive) invariant conditions into constraints. The problem of characterizing the set of all valid parameter assignments is referred to as the strong invariant synthesis problem , while the problem of finding a concrete valid parameter assignment is called the weak invariant synthesis problem . For both problems, the challenge lies in solving or reducing the encoded constraints, which are generally non-convex and lack efficient solvers. In this paper, we propose two novel algorithms for synthesizing invariants of polynomial programs using semidefinite programming (SDP): (1) The Cluster algorithm targets the strong invariant synthesis problem for polynomial invariant templates. Leveraging robust optimization techniques, it solves a series of SDP relaxations and yields a sequence of increasingly precise under-approximations of the set of valid parameter assignments. We prove the algorithm’s soundness, convergence, and weak completeness under a specific robustness assumption on templates. Moreover, the outputs can simplify the weak invariant synthesis problem. (2) The Mask algorithm addresses the weak invariant synthesis problem in scenarios where the aforementioned robustness assumption does not hold, rendering the Cluster algorithm ineffective. It identifies a specific subclass of invariant templates, termed masked templates, involving parameterized polynomial equalities and known inequalities. By applying variable substitution, the algorithm transforms constraints into an equivalent form amenable to SDP relaxations. Both algorithms have been implemented and demonstrated superior performance compared to state-of-the-art methods in our empirical evaluation.

Hao Wu

Qiuye Wang

Bai Xue

Naijun Zhan

Lihong Zhi

Zhi-Hong Yang

ACM Transactions on Programming Languages and Systems

ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS (TOPLAS) 是报告编程语言领域最新研究进展的主要期刊，以及协助编程任务的系统。论文的风格可以是理论性的，也可以是实验性的，但无论哪种情况，它们都必须包含创新和新颖的内容，以推动编程语言和系统的最新发展。我们还邀请严格比较现有方法的实验论文，以及教程和调查论文。 TOPLAS 的范围包括但不限于以下主题： 用于顺序和并行编程的语言设计 编程语言实现 编程语言语义 编译器和解释器 用于程序执行存储分配和垃圾收集的运行时系统 用于编写程序规范的语言和方法 语言安全可靠的程序测试和程序验证方法及方法

The ACM Transactions on Programming Languages and Systems (TOPLAS) is a leading journal that reports on the latest research advancements in the field of programming languages and the systems that support programming tasks. The journal welcomes both theoretical and experimental papers, provided they contain innovative and novel content that advances the state of programming languages and systems. We also invite experimental papers that rigorously compare existing methods, as well as tutorial and survey papers. The scope of TOPLAS includes, but is not limited to, the following topics: language design for sequential and parallel programming, implementation of programming languages, semantics of programming languages, compilers and interpreters, runtime systems for program execution, memory allocation and garbage collection, languages and methods for writing program specifications, language safety, reliable program testing, and program verification methods.

《ACM Transactions on Programming Languages and Systems》（TOPLAS）是编程语言领域最新研究成果的重要期刊，致力于支持编程任务的系统研究。该期刊接受理论性和实验性的论文，但无论是哪种类型，论文都必须包含创新和新颖的内容，以推动编程语言和系统的发展。我们还欢迎对现有方法进行严格比较的实验论文，以及教程和调查性论文。TOPLAS的研究范围包括但不限于以下主题：顺序和并行编程的语言设计、编程语言的实现、编程语言的语义、编译器和解释器、用于程序执行的存储分配和垃圾收集的运行时系统、用于编写程序规范的语言和方法、语言安全性、可靠的程序测试和程序验证的方法。

Category	Quartile
计算机科学	2
计算机科学, 计算机软件工程	2

Synthesizing Invariants for Polynomial Programs by Semidefinite Programming

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Journal Info

Category	Quartile
COMPUTER SCIENCE, SOFTWARE ENGINEERING	3