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.

Qualitative numeric planning (QNP) is classical planning extended with non-negative real variables that can be increased or decreased by some arbitrary amount. Existing approaches for solving QNP problems are exclusively based on compilation to fully observable nondeterministic planning (FOND) problems or FOND+ problems, i.e., FOND problems with explicit fairness assumptions. However, the FOND-compilation approaches suffer from some limitations, such as difficulties to generate all strong cyclic solutions for FOND problems or introducing a great many extra variables and actions. In this paper, we propose a simpler characterization of QNP solutions and a new approach to solve QNP problems based on directly searching for a solution, which is a closed and terminating subgraph that contains a goal node, in the AND/OR graphs induced by QNP problems. Moreover, we introduce a pruning strategy based on termination tests on subgraphs. We implemented a native solver DSET based on the proposed approach and compared the performance of it with that of the two compilation-based approaches. Experimental results show that DSET is faster than the FOND-compilation approach by one order of magnitude, and comparable with the FOND+-compilation approach.