The computational complexity of propositional STRIPS planning
Artificial Intelligence
Automatically generating abstractions for planning
Artificial Intelligence
Downward refinement and the efficiency of hierarchical problem solving
Artificial Intelligence
Tractable plan existence does not imply tractable plan generation
Annals of Mathematics and Artificial Intelligence
Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
A reactive planner for a model-based executive
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
Structure and complexity in planning with unary operators
Journal of Artificial Intelligence Research
The complexity of planning problems with simple causal graphs
Journal of Artificial Intelligence Research
Planning over chain causal graphs for variables with domains of size 5 Is NP-hard
Journal of Artificial Intelligence Research
The role of macros in tractable planning
Journal of Artificial Intelligence Research
A refined view of causal graphs and component sizes: SP-closed graph classes and beyond
Journal of Artificial Intelligence Research
Hi-index | 0.00 |
Causal graphs are widely used in planning to capture the internal structure of planning instances. Researchers have paid special attention to the subclass of planning instances with acyclic causal graphs, which in the past have been exploited to generate hierarchical plans, to compute heuristics, and to identify classes of planning instances that are easy to solve. This naturally raises the question of whether planning is easier when the causal graph is acyclic. In this article we show that the answer to this question is no, proving that in the worst case, the problem of plan existence is PSPACE-complete even when the causal graph is acyclic. Since the variables of the planning instances in our reduction are propositional, this result applies to Strips planning with negative preconditions. We show that the reduction still holds if we restrict actions to have at most two preconditions. Having established that planning is hard for acyclic causal graphs, we study two subclasses of planning instances with acyclic causal graphs. One such subclass is described by propositional variables that are either irreversible or symmetrically reversible. Another subclass is described by variables with strongly connected domain transition graphs. In both cases, plan existence is bounded away from PSPACE, but in the latter case, the problem of bounded plan existence is hard, implying that optimal planning is significantly harder than satisficing planning for this class.