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The complexity of ordering subgoals

Selection of an appropriate order for the evaluation of subgoals in a logical rule frequently is essential for efficiency. We formulate the problem as one of feasible subgoal orders and show that the question is inherently exponential in time. The proof is by reduction from linear-space alternating Turing machine recognition, which appears to be far easier, in this case, than the more obvious reduction from exponential-time (ordinary) Turing machines