Complexity, decidability and undecidability results for domain-independent planning
Artificial Intelligence - Special volume on planning and scheduling
Approximate reasoning about actions in presence of sensing and incomplete information
ILPS '97 Proceedings of the 1997 international symposium on Logic programming
Probabilistic propositional planning: representations and complexity
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Planning under Incomplete Knowledge
CL '00 Proceedings of the First International Conference on Computational Logic
CL '00 Proceedings of the First International Conference on Computational Logic
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In the last several years the computational complexity of classical planning and HTN planning have been studied. But in both cases it is assumed that the planner has complete knowledge about the initial state. 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 1993 by M. Gelfond and V. Lifschitz and its extensions. The language A allows planning in the situations with complete information. It is known that, if we consider only plans of feasible (polynomial) length, the planning problem for such situations 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 Σ2P-complete). To overcome the complexity of this problem, C. Baral and T. Son have proposed several approximations. We show that under certain conditions, one of these approximations - O-approximation - makes the problem NP-complete (thus indeed reducing its complexity).