In this article we study and evaluate combinatorial algorithms for exploring state spaces of prototypical artificial intelligence problems that are represented by very large state space graphs. We are interested in the modeling and analysis of such graphs, including their visualization and quantification. We consider Blocks World as a prototype artificial intelligence problem that is often employed to introduce problem solving strategies using searching, planning, and reasoning algorithms. Our results are mathematical models and combinatorial algorithms supporting the concise definition of the Blocks World state space graph, as well as the exact evaluation of several metrics defined on this graph, including its number of states, its average number of stacks per state, its number of transitions, and its average branching factor. We also present experimental results supporting the effectiveness and efficiency of our proposed algorithms.

中文翻译：

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探索 Blocks World 状态空间

在本文中，我们研究和评估用于探索由非常大的状态空间图表示的原型人工智能问题的状态空间的组合算法。我们对此类图的建模和分析感兴趣，包括它们的可视化和量化。我们将 Blocks World 视为一个原型人工智能问题，通常用于引入使用搜索、规划和推理算法的问题解决策略。我们的结果是支持 Blocks World 状态空间图的简明定义的数学模型和组合算法，以及对该图上定义的几个指标的精确评估，包括它的状态数、每个状态的平均堆栈数、它的数量的转换，以及它的平均分支因子。