Computational Complexity of Jumping Block Puzzles

In combinatorial reconfiguration, the reconfiguration problems on a vertex subset (e.g., an independent set) are well investigated. these problems, some tokens placed of vertices graph, and there three natural rules called ``token sliding,'' jumping,'' addition removal''. context computational complexity puzzles, sliding block puzzles play important role. Depending set pieces, characterize classes including P, NP, PSPACE. The correspond to token model in reconfiguration. On other hand, relatively new notion jumping is proposed puzzle society. This counterpart puzzles. We investigate several variants determine their complexities.