This paper addresses the exponential state explosion in heuristic planning by introducing indexical policies, which use registers and modes to sequence rules. A new choose rule allows the system to load objects and mark backtracking points, ensuring that only one candidate needs to be pursued at each step while other rules apply universally. This structural approach guarantees that execution length is bounded by a polynomial relative to the number of objects, enabling a depth-first search procedure that operates in polynomial space regardless of the total state space size.
- Indexical policies replace explicit state storage with generalized rules using registers.
- The choose rule limits backtracking to single candidates, reducing search overhead.
- Structural termination proofs ensure execution length remains polynomial in object count.
- Depth-first search achieves polynomial space complexity even with vast state spaces.