A Probabilistic Analysis of Propositional STRIPS Planning

I present a probabilistic analysis of propositional STRIPS planning. The analysis considers two assumptions. One is that each possible precondition (likewise postcondition) of an operator is selected independently of other pre-and postconditions. The other is that each operator has a xed number of preconditions (likewise postconditions). Under both assumptions , I derive bounds for when it is highly likely that a planning instance can be eeciently solved, either by nding a plan or proving that no plan exists. Roughly, if planning instances under either assumption have n propositions (ground atoms) and g goals, and the number of operators is less than an O(n ln g) bound, then a simple, eecient algorithm can prove that no plan exists for most instances. If the number of operators is greater than an (n ln g) bound, then a simple, eecient algorithm can nd a plan for most instances. The two bounds diier by a factor that is exponential in the number of pre-and postconditions. A similar result holds for plan modiication, i.e., solving a planning instance that is close to another planning instance with a known plan. Thus it appears that propositional STRIPS planning, a PSPACE-complete problem, exhibits a easy-hard-easy pattern as the number of available operators increases with a narrow range of hard problems. An empirical study demonstrates this pattern for particular parameter values. Because propositional STRIPS planning is PSPACE-complete, this extends previous phase transition analyses, which have focused on NP-complete problems. Also, the analysis shows that surprisingly simple algorithms can solve a large subset of the planning problems. This paper is a revised and extended version of 4].