Quantitative verification of software families based on coalgebraic modal logic and games

基于联代数模态逻辑和博弈的软件族定量验证

• 批准号: EP/X019373/1
• 负责人: Harsh Beohar
• 金额: $ 30.05万
• 依托单位: University of Sheffield
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FX019373%2F1
• 关键词: Quantitative; verification; software; families; based

To facilitate software with mass customisation, many software vendors develop a product from a core software base. As a result, it has become increasingly common to consider not only a single product, but to model and develop a family of software systems at the same time. Now this transformation of designing a single product to a family of software systems poses, in general, two significant challenges for Formal Methods. First, the traditional formal verification techniques for establishing conformance on a single product suffers from scalability since the inability of underlying formalisms to express behaviour of a software family. Second, conformance when stated as an equivalence relation is not a robust notion of behavioural comparison w.r.t. a specification, where a more fine-grained comparison in the form of behavioural distance is required. This is particularly relevant when software includes components that interact with an uncertain environment (like in the context of autonomous driving) and the correctness of such safety-crticial systems is part of the global trend on explainable AI.So our overarching aim is to advance the state-of-art verification techniques by enabling a more fine-grained behavioural analysis of software families based on behavioural distances. In particular, we will develop abstract mathematical models to specify behaviour of software families, develop fixpoint algorithms to compute behavioural distances on such models, and develop analysis technqiues to diagnose when an implementation is nonconforming. Building upon our recent work on behavioural equivalences for software families, we will pose and tackle our research questions at the abstract level of coalgebras. The advantage is that one can create a generic core framework to reason about a family of state-based systems of fixed branching types, which can be instantiated to concrete domains like software product lines (both static or adaptive) or parametric Markov models. In other words, this proposal lays out the theoretical underpinning necessary for the quantitative verification of software families modelled as coalgebras. Furthermore, this research also provides an impetus for evolving the theory of coalgebras since many fundamental questions (like expressive modal logics and games) for behavioural distances on coalgebras with side effects are not yet developed.

为了促进软件大规模定制，许多软件供应商从核心软件库开发产品。因此，不仅考虑单个产品，而且同时建模和开发一系列软件系统已变得越来越普遍。现在，这种从单一产品设计到一系列软件系统的转变总体上给形式化方法带来了两个重大挑战。首先，用于在单个产品上建立一致性的传统形式验证技术受到可扩展性的影响，因为底层形式主义无法表达软件系列的行为。其次，当将一致性表述为等价关系时，一致性并不是行为比较的稳健概念。一个规范，需要以行为距离的形式进行更细粒度的比较。当软件包含与不确定环境交互的组件（例如在自动驾驶的情况下）并且此类安全关键系统的正确性是可解释人工智能全球趋势的一部分时，这一点尤其重要。因此，我们的首要目标是推进通过基于行为距离对软件系列进行更细粒度的行为分析来实现最先进的验证技术。特别是，我们将开发抽象数学模型来指定软件系列的行为，开发固定点算法来计算此类模型的行为距离，并开发分析技术来诊断实施何时不合格。基于我们最近关于软件系列行为等价性的工作，我们将在余代数的抽象层面提出并解决我们的研究问题。优点是可以创建一个通用核心框架来推理一系列基于状态的固定分支类型系统，这些系统可以实例化为具体领域，例如软件产品线（静态或自适应）或参数马尔可夫模型。换句话说，该提案奠定了对建模为余代数的软件族进行定量验证所需的理论基础。此外，这项研究还为余代数理论的发展提供了动力，因为关于具有副作用的余代数行为距离的许多基本问题（如表达模态逻辑和博弈）尚未得到发展。

项目成果

Hennessy-Milner Theorems via Galois Connections

通过伽罗瓦连接的 Hennessy-Milner 定理

• DOI: 10.4230/lipics.csl.2023.12
• 发表时间: 2023
• 作者: Beohar H