A Spatial Lexical Analyzer and 3D Grammars that Recognize Voxel Based Structures Using Linear Positional Grammars in Minecraft

We introduce the use of 3D grammars for the identification of objects formed by voxels, i.e., discrete element cells that compose a 3D grid. We also show how to apply these grammars in a bot that can recognize structures in Minecraft. Our main contribution is a new spatial lexical analyzer that can decide the direction it must follow to obtain the next input by looking at the future positions and the expected next token in a Linear Positional Grammar. Moreover, we define different positional relations and specific grammars for various Minecraft structures.