Towards efficient universal planning: A randomized approach

One of the most widespread approaches to reactive planning is Schoppers universal plans We propose a stricter de nition of univer sal plans which guarantees a weak notion of soundness not present in the original de nition and isolate three di erent types of complete ness that capture di erent behaviors exhibited by universal plans We show that universal plans which run in polynomial time and are of polynomial size cannot satisfy even the weakest type of completeness unless the polynomial hierarchy collapses By relaxing either the poly nomial time or the polynomial space requirement the construction of universal plans satisfying the strongest type of completeness becomes trivial As an alternative approach we study randomized universal planning By considering a randomized version of completeness and a restricted but nontrivial class of problems we show that there ex ists randomized universal plans running in polynomial time and using polynomial space which are sound and complete for the restricted class of problems We also report experimental results on this approach to planning showing that the performance of a randomized planner is not easily compared to that of a deterministic planner