Exploring the Blocks World state space

In this article we study and evaluate combinatorial algorithms for exploring state spaces of prototypical artificial intelligence problems that are represented by very large state space graphs. We are interested in the modeling and analysis of such graphs, including their visualization and quantification. We consider Blocks World as a prototype artificial intelligence problem that is often employed to introduce problem solving strategies using searching, planning, and reasoning algorithms. Our results are mathematical models and combinatorial algorithms supporting the concise definition of the Blocks World state space graph, as well as the exact evaluation of several metrics defined on this graph, including its number of states, its average number of stacks per state, its number of transitions, and its average branching factor. We also present experimental results supporting the effectiveness and efficiency of our proposed algorithms.