A constructive proof for the subsets completeness of 8-puzzle state space
Xin Ma · 2010
Based on the mathematical analysis, the accessibility between various states in 8-puzzle state space is discussed in this paper. A necessary and sufficient condition in which the states can be transformed into each other is proposed, and its correctness is proved. On the basis of which, a complete mathematical structure of the 8-puzzle state space is esta-blished by utilizing the accessible relation as an equivalence relation. Furthermore, a valid deduction is given, that is, for the 7 numbers that are in a Style Box, each of their states can be transformed into each other.