text: abstract
  the pancake puzzle is a classic optimization problem that has become a standard benchmark for heuristic search
  algorithms. in this paper, we provide full proofs regarding the local search topology of the gap heuristic for the
  pancake puzzle. first, we show that in any non-goal state in which there is no move that will decrease the number of
  gaps, there is a move that will keep the number of gaps constant. we then classify any state in which the number of
  gaps cannot be decreased in a single action into two groups: those requiring 2 actions to decrease the number of gaps,
  and those which require 3 actions to decrease the number of gaps.