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Why is the delete relaxation solvable in polynomial time?

  • A.Actions in the relaxed problem have no preconditions at all
  • B.Facts once achieved are never lost, so no backtracking is needed
  • C.The relaxed problem contains fewer actions than the original
  • D.The goal of the relaxed problem is always immediately satisfied anyway

Answer: B

Because nothing is ever deleted, the set of achievable facts grows monotonically and can be computed by a fixed point iteration, so no choice among actions can ever be regretted. Action counts and preconditions are unchanged and the goal is not automatically met. Monotonicity removing the need for search is the same property that makes forward chaining over definite clauses linear, appearing here in a different guise.

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