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The merge-and-shrink framework is a powerful tool for constructing state-of-the-art admissible heuristics in classical planning. Recent work has begun generalizing the complex theory behind this framework to probabilistic planning in forms of stochastic shortest-path problems (SSPs). There however remain two important gaps. Firstly, although the previous work makes substantial efforts, the probabilistic merge-and-shrink theory is still incomplete, lacking in particular prune transformations, i.e., transformations discarding uninteresting states, effectively reducing the size of the abstraction without losing relevant information. Secondly, an actual implementation and experimental evaluation of the merge-and-shrink framework for SSPs is so far missing. Here, we round off the previous work by contributing both a theoretical analysis of prune transformations, as well as an empirical evaluation of merge-and-shrink heuristics. Our results show that merge-and-shrink heuristics outperform previous single abstraction heuristics, but do not quite reach the performance of state-of-the-art additive combinations of such heuristics yet.
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