Since Kautz and Selman's 1992 ECAI paper on satisability based planning, there has been several work on planning through nding models of a logical theory. Most of these works focus on nding a plan of a given length. If we w ant to nd the shortest plan, then usually, w e try plans of length 1, 2, . . . , until we n d the rst length for which s u c h a plan exists. When the planning problem is di cult and the shortest plan is of a reasonable length, this linear search can take a l o n g time to speed up the process, it has been proposed (by Lifschitz and others) to use binary search instead. Binary search for the value of a certain parameter x is optimal when for each tested value x, w e need the same amount of computation time in planning, the computation time increases with the size of the plan and, as a result, binary search is no longer optimal. We describe an optimal way of combining planning algorithms into a search for the shortest plan { optimal in the sense of worst-case complexity. We also describe an algorithm which is asymptotically optimal in the sense of average complexity.
Abstract. We present a state-based regression function for planning domains where an agent does not have complete information and may have sensing actions. We consider binary domains and employ a three-valued characterization of domains with sensing actions to define the regression function. We prove the soundness and completeness of our regression formulation with respect to the definition of progression. More specifically, we show that (i) a plan obtained through regression for a planning problem is indeed a progression solution of that planning problem, and that (ii) for each plan found through progression, using regression one obtains that plan or an equivalent one.
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