Expressive Equivalence of Formalisms for Planning with Sensing

There have been several proposals for expressing planning problems with different forms of uncertainty, including nondeterminism and partial observability. In this paper we investigate two questions. First, the restriction to certain normal forms of operators, for example, restricting to operators in which nondeterministic choice must be outside conditional effects, or vice versa. We show that some such restrictions lead to an exponentially less succinct representation of problem instances. Second, we consider the problem of reducing certain features of formalisms for planning problem to other, more basic features. We show that compound observations can be reduced to atomic observations, sensing uncertainty can be reduced to effect uncertainty, dependence of observations on the operator last applied (special sensing actions) can be reduced to the case in which same observations are always possible. We show that these reductions are possible without significantly affecting quantitative properties of problem instances. One reduction doubles plan length, and the others do not affect plan length and only increase problem instance size slightly.