An Automatic Sound and Complete Abstraction Method for Generalized Planning with Baggable Types

TL;DR

This paper introduces an automatic method for creating sound and complete abstractions for generalized planning problems involving baggable types, using a variant of QNP called BQNP, with practical implementation and experimental validation.

Contribution

It proposes a novel automatic abstraction technique for generalized planning with baggable types using BQNP, ensuring soundness and completeness for proper domains.

Findings

The method produces sound and complete abstractions for proper baggable domains.

Experiments demonstrate the effectiveness of the approach across multiple domains.

The solver for BQNP is sound but incomplete, suitable for practical use.

Abstract

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.