Probabilistic Propositional Planning: Representations and Complexity
Many representations for probabilistic propositional planning problems have been studied. This paper reviews several such representations and shows that, in spite of superficial differences between the representations, they are "expressively equivalent," meaning that planning problems specified in one representation can be converted to equivalent planning problems in any of the other representations with at most a polynomial factor increase in the size of the resulting representation and the number of steps needed to reach the goal with sufficient probability. The paper proves that the computational complexity of determining whether a successful plan exists for planning problems expressed in any of these representations is EXPTIME-complete and PSPACE-complete when plans are restricted to take a polynomial number of steps.