On the Hardness of Planning Problems with Simple Causal Graphs

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We present three new complexity results for classes of planning problems with simple causal graphs. First, we describe a polynomial time algorithm that uses macros to generate plans for a class of planning problems with binary state variables and acyclic causal graphs. This implies that plan generation may not be intractable just because a planning problem has exponential length solution. We also prove that the problem of plan existence for planning problems with multi-valued variables and chain causal graphs is NP-hard. Finally, we show that plan existence for planning problems with binary state variables and polytree causal graphs is NP-complete.