针对具有可装包类型的广义规划的一种自动且可靠完备的抽象方法
An Automatic Sound and Complete Abstraction Method for Generalized Planning with Baggable Types
AI总结：
针对广义规划自动抽象难以保证可靠性和完备性的问题，提出一种基于有界QNP（BQNP）的自动可靠且完备的抽象方法，通过为不可区分对象元组引入计数器，证明了在适当可装包域中精炼规划可解决原问题，实验验证了其有效性。
摘要：
广义规划关注如何找到单一规划来解决多个相似的规划实例。抽象被广泛用于解决广义规划，而QNP（定性数值规划）是一种流行的抽象模型。最近，Cui等人表明，当且仅当精炼规划解决原始问题时，该规划解决的是广义规划问题的可靠且完备的抽象。然而，现有的关于广义规划自动抽象的工作很难保证可靠性，更不用说完备性了。在本文中，我们提出了一种针对具有可装包类型的广义规划的自动可靠且完备的抽象方法。我们使用QNP的一种变体，称为有界QNP（BQNP），其中整数变量仅增加或减少1。由于BQNP是不可判定的，我们提出并实现了一个可靠但不完备的BQNP求解器。我们提出了一种自动方法，从具有可装包类型的经典规划实例中抽象出BQNP问题。抽象的基本思想是为每袋不可区分的对象元组引入一个计数器。我们定义了一类称为适当可装包域的域，并表明对于此类域，通过我们的自动方法获得的BQNP问题是广义规划问题的可靠且完备的抽象，该广义规划问题的实例与给定实例共享相同的袋，但袋的大小可能不同。因此，BQNP问题解的精炼规划是广义规划问题的解。最后，我们实现了我们的抽象方法，在多个域上的实验展示了我们方法的潜力。
英文摘要：
Generalized planning is concerned with how to find a single plan to solve multiple similar planning instances. Abstractions are widely used for solving generalized planning, and QNP (qualitative numeric planning) is a popular abstract model. Recently, Cui et al. showed that a plan solves a sound and complete abstraction of a generalized planning problem if and only if the refined plan solves the original problem. However, existing work on automatic abstraction for generalized planning can hardly guarantee soundness let alone completeness. In this paper, we propose an automatic sound and complete abstraction method for generalized planning with baggable types. We use a variant of QNP, called bounded QNP (BQNP), where integer variables are increased or decreased by only one. Since BQNP is undecidable, we propose and implement a sound but incomplete solver for BQNP. We present an automatic method to abstract a BQNP problem from a classical planning instance with baggable types. The basic idea for abstraction is to introduce a counter for each bag of indistinguishable tuples of objects. We define a class of domains called proper baggable domains, and show that for such domains, the BQNP problem got by our automatic method is a sound and complete abstraction for a generalized planning problem whose instances share the same bags with the given instance but the sizes of the bags might be different. Thus, the refined plan of a solution to the BQNP problem is a solution to the generalized planning problem. Finally, we implement our abstraction method and experiments on a number of domains demonstrate the promise of our approach.
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