Why Letter Substitution Puzzles are Not Hard to Solve: A Case Study in Entropy and Probabilistic Search-Complexity

In this paper we investigate the theoretical causes of the disparity between the theoretical and practical running times for the A∗ algorithm proposed in Corlett and Penn (2010) for deciphering letter-substitution ciphers. We argue that the difference seen is due to the relatively low entropies of the probability distributions of character transitions seen in natural language, and we develop a principled way of incorporating entropy into our complexity analysis. Specifically, we find that the low entropy of natural languages can allow us, with high probability, to bound the depth of the heuristic values expanded in the search. This leads to a novel probabilistic bound on search depth in these tasks.