Macro-operators: a weak method for learning
Artificial Intelligence - Lecture notes in computer science 178
A formalization of explanation-based macro-operator learning
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 2
On linear logic planning and concurrency
Information and Computation
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Korf (1985) presents a method for learning macro-operators and shows that the method is applicable to serially decomposable problems. In this paper I analyze the computational complexity of serial decomposability. Assuming that operators take polynomial time, it is NP-complete. to determine if an operator (or set of operators) is not serially decomposable, whether or not an ordering of state variables is given. In addition to serial decomposability of operators, a serially decomposable problem requires that the set of solvable states is closed under the operators. It is PSPACE-complete to determine if a given "finite state-variable problem" is serially decomposable. In fact, every solvable instance of a PSPACE problem can be converted to a serially decomposable problem. Furthermore, given a bound on the size of the input, every problem in PSPACE can be transformed to a problem that is nearly serially-decomposable, i.e., the problem is serially decomposable except for closure of solvable states or a unique goal state.