Application of a Limit Theorem to the Construction of Japanese Crossword Puzzles

The generation of crossword puzzles is known to be NP-Complete. Optimization over structural characteristics is known to extend this into the NP-Hard regime. This paper discusses the application of a limit theorem to assist in optimizing the NP-Hard aspects of crossword puzzle generation of Japanese lexicons in particular. It is shown that the similarity of artificially enumerated lexicons to Japanese kana-based lexicons is greater than to English language lexicons. This greater similarity is exploited in the derivation of expressions for both the expected value of the crossword and the use of the central limit theorem to determine an empirical estimate on the upper limit of the associated optimization problem. Initial empirical outcomes attest to the expected efficacy of the central limit theorem application to the final expressions.