Computational Complexity of Planning and Approximate Planning in Presence of Incompleteness

In the last several years, there have been several studies about the computational complexity of classical planning assuming that the planner has complete knowledge about the initial situation. Recently, there has been proposal to use sensing actions to plan in presence of incompleteness. In this paper we study the complexity of planning in such cases. In our study we use the action description language A proposed in 1991 by Gelfond and Lifschitz, and its extensions. It is known that if we consider only plans of feasible (polynomial) length, planning - with complete information about the initial situation - in A is NP-complete: even checking whether a given objective is attainable from a given initial state is NP-complete. In this paper, we show that the planning problem in presence of incompleteness is indeed harder: it belongs to the next level of complexity hierarchy (in precise terms, it is Sigma_2 P-complete). To overcome the complexity of this problem, Baral and Son have proposed several approximations. We show that under certain conditions, one of these approximations - 0-approximation - makes the problem NP-complete (thus indeed reducing its complexity)