arXiv subjects

Shushu Wu

Publications and source records attributed to Shushu Wu.

3 recordsLinked to original sources

arXiv2025

QCP: A Practical Separation Logic-based C Program Verification Tool

As software systems increase in size and complexity dramatically, ensuring their correctness, security, and reliability becomes an increasingly formidable challenge. Despite significant advancements in verification techniques and tools, their practical application to complex, real-world systems is often hindered by critical gaps in both automation and expressiveness. To address these difficulties, this paper presents \textbf{Qualified C Programming Verifier (QCP)}, a novel verification tool that integrates annotation-based automatic verification with interactive proving using Rocq. QCP employs symbolic execution and a separation logic entailment solver to automatically discharge many verification obligations, while deferring more complex obligations to Rocq for manual proof. Furthermore, QCP includes a VS Code extension designed to enhance proof efficiency and support a deeper understanding of both the program behavior and verification outcomes.

cs.PL↗

arXiv2025

A Formal Framework for Naturally Specifying and Verifying Sequential Algorithms

Current approaches for formal verification of algorithms face important limitations. For specification, they cannot express algorithms naturally and concisely, especially for algorithms with states and flexible control flow. For verification, formal proof based on Hoare logic cannot reflect the logical structure of natural proof. To address these challenges, we introduce a formal framework for naturally specifying and verifying sequential algorithms in Coq. We use the state relation monad to integrate Coq's expressive type system with the flexible control flow of imperative languages. It supports nondeterministic operations and customizable program states, enabling specifying algorithms at an appropriate level of abstraction. For verification, we build a Hoare logic for the monad and propose a novel two-stage proof approach that separates natural logical reasoning from mechanical composition. It reflects the logical structure of natural proof, enhancing modularity and readability. We evaluate the framework by formalizing the Depth-First Search (DFS) algorithm and verifying the Knuth-Morris-Pratt (KMP) algorithm.

cs.PL↗

arXiv2025

Encode the $\forall\exists$ Relational Hoare Logic into Standard Hoare Logic

Verifying a real-world program's functional correctness can be decomposed into (1) a refinement proof showing that the program implements a more abstract high-level program and (2) an algorithm correctness proof at the high level. Relational Hoare logic serves as a powerful tool to establish refinement but often necessitates formalization beyond standard Hoare logic. Particularly in the nondeterministic setting, the $\forall\exists$ relational Hoare logic is required. Existing approaches encode this logic into a Hoare logic with ghost states and invariants, yet these extensions significantly increase formalization complexity and soundness proof overhead. This paper proposes a generic encoding theory that reduces the $\forall\exists$ relational Hoare logic to standard (unary) Hoare logic. Precisely, we propose to redefine the validity of relational Hoare triples while preserving the original proof rules and then encapsulate the $\forall\exists$ pattern within assertions. We have proved that the validity of encoded standard Hoare triples is equivalent to the validity of the desired relational Hoare triples. Moreover, the encoding theory demonstrates how common relational Hoare logic proof rules are indeed special cases of standard Hoare logic proof rules, and relational proof steps correspond to standard proof steps. Our theory enables standard Hoare logic to prove $\forall\exists$ relational properties by defining a predicate Exec, without requiring modifications to the logic framework or re-verification of soundness.

cs.PL↗