Binary decision diagrams can compactly represent vast sets of states, mitigating the state space explosion problem in model checking. Probabilistic systems, however, require multi-terminal diagrams storing rational numbers. They are inefficient for models with many distinct probabilities and for iterative numeric algorithms like value iteration. In this paper, we present a new "symblicit" approach to checking Markov chains and related probabilistic models: We first generate a decision diagram that symbolically collects all reachable states and their predecessors. We then concretise states one-by-one into an explicit partial state space representation. Whenever all predecessors of a state have been concretised, we eliminate it from the explicit state space in a way that preserves all relevant probabilities and rewards. We thus keep few explicit states in memory at any time. Experiments show that very large models can be model-checked in this way with very low memory consumption.

中文翻译：

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用于概率模型检查的符号探索和消除

二元决策图可以紧凑地表示大量状态，减轻模型检查中的状态空间爆炸问题。然而，概率系统需要存储有理数的多端图。它们对于具有许多不同概率的模型和迭代数值算法（如值迭代）效率低下。在本文中，我们提出了一种新的“符号”方法来检查马尔可夫链和相关概率模型：我们首先生成一个决策图，该图象征性地收集了所有可达状态及其前身。然后我们将状态一一具体化为显式的部分状态空间表示。每当一个状态的所有前驱都被具体化时，我们以保留所有相关概率和奖励的方式将其从显式状态空间中消除。因此，我们在任何时候都会在内存中保留很少的显式状态。实验表明，非常大的模型可以通过这种方式以非常低的内存消耗进行模型检查。