Blocks world

The blocks world is one of the most famous planning domains in artificial intelligence. Imagine a set of wooden blocks of various shapes and colors sitting on a table. The goal is to build one or more vertical stacks of blocks. The catch is that only one block may be moved at a time: it may either be placed on the table or placed atop another block. Because of this, any blocks that are, at a given time, under another block cannot be moved. Moreover, some kinds of blocks cannot have other blocks stacked on top of them.

The simplicity of this toy world lends itself readily to symbolic or classical A.I. approaches, in which the world is modeled as a set of abstract symbols which may be reasoned about.

Decision problem (Gupta and Nau, 1992): Given a starting Blocks World, an ending Blocks World, and an integer L > 0, is there a way to move the blocks to change the starting position to the ending position with L or less steps?

This decision problem is NP-hard.

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