Counterexample-guided abstraction refinement (CEGAR) is an extremely successful methodology for combating the state-space explosion problem in model checking. State-space explosion problem is more serious in the field of stochastic model checking, and it is still a challengeable problem to apply CEGAR in stochastic model checking effectively. In this paper, we formalize the problem of applying CEGAR in stochastic model checking, and propose a novel CEGAR framework for it. In our framework, the abstract model is presented by a quotient probabilistic automaton by making a set of variables or latches invisible, which can distinguish more degrees of abstraction for each variable. The counterexample is described by a diagnostic sub-model. Validating counterexample is performed on diagnostic loop paths, and the directed explicit state-space search algorithm is used for searching diagnostic loop paths. Sample learning, particle swarm optimization algorithm (PSO) and some effective heuristics are integrated for refining abstract model guided by invalid counterexample. A prototype tool is implemented for the framework, and the feasibility and efficiency are shown by some large cases.

中文翻译：

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用于随机模型检查的基于 PSO 的 CEGAR 框架

反例引导的抽象细化（CEGAR）是一种非常成功的方法，用于解决模型检查中的状态空间爆炸问题。状态空间爆炸问题在随机模型检验领域更为严重，如何有效地将CEGAR应用于随机模型检验仍是一个具有挑战性的问题。在本文中，我们形式化了在随机模型检查中应用 CEGAR 的问题，并为此提出了一个新的 CEGAR 框架。在我们的框架中，抽象模型由商概率自动机通过使一组变量或锁存器不可见来呈现，这可以区分每个变量的更多抽象程度。反例由诊断子模型描述。在诊断循环路径上执行验证反例，使用有向显式状态空间搜索算法搜索诊断回路路径。将样本学习、粒子群优化算法（PSO）和一些有效的启发式算法相结合，用于提炼无效反例引导的抽象模型。该框架实现了一个原型工具，并通过一些大型案例展示了其可行性和效率。