6 Conclusion and Related Work Problem Dimension (# of Locations) Size of State Action Table Hunter Hunter Universal Hunter Cycle Beam

17 changes through the use of non-inertial uents and releases the user from the task of describing the eeects of the law of inertia. Problem descriptions in AR are very concise and simple, compared with the corresponding au-tomata see for instance the simple example in gures 1 and 2. Dean et al., 1995 describes an algorithm which can be used for anytime planning, by nding the solution for a restricted state space and then increasing iteratively the state space which is considered. Our algorithm searches for a solution backward from the goal to the initial states. It would be interesting to apply the same kind of strategy used in Dean et al., 1995 within our approach, for instance by searching rst for a weak solution, and then extending it step-by-step with state-action pairs returned by the StrongPreImage. Acknowledgments We thank Marco Daniele for nding a bug in an early version of the planning algorithm. 16 number of states. This hypothesis, though quite strong, allows us to treat many signiicant planning problems. Second, the algorithm presented in this paper can be signiicantly optimized. For instance, when looking for cycles which can lead to a set of states in n steps, it does not make use of the previous computations searching for loops which can lead to the set of states in n,1 steps. Moreover, it does not fully exploit several existing model current search strategy is committed to one particular notion of optimality, i.e. it looks rst for strong solutions. This might not be the most natural strategy for all the application domains. Finally, w e do not have the complete assurance that the approach can scale up to very complex problems. Even if the preliminary results are promising, and even if symbolic model checking has been shown to do well in complex industrial veriication tasks, we still need to experiment with extensive tests and with real-world large-scale applications. Only few previous works address the automatic generation of universal plans in domains which are not deterministic. In Kabanza, Barbeau, & St-Denis, 1997, a planning algorithm searches the non-deterministic automaton representing the domain in order to solve complex goals speciied as temporal logic formulae. The approach is based on explicit state search, and heuristics are required to contain the state explosion problem. Koenig and Simmons Koenig & Simmons, 1995 describe an extension of real-time search called min-max LRTA to deal with non-deterministic …