Abstracting the Tower of Hanoi

ing the Tower of Hanoi Craig A. Knoblock School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 [email protected] Abstract This paper describes an automated approach to generating abstractions for the Tower of Hanoi and analyzes the use of these abstractions for problem solving. The analysis shows that the learned abstractions produce an exponential reduction in the size of the search space. Since few problem solvers actually explore the entire search space, the paper also presents an empirical analysis of the speedup provided by abstraction when a heuristic search is employed. The empirical analysis shows that the bene t of abstraction is largely determined by the portion of the base-level search space explored. Thus, using breadthrst search, which searches the entire space, abstraction provides an exponential reduction in search. However, using a depthrst search, the search reduction is smaller and depends on the amount of backtracking required to solve the problem. Abstractions, 1990This paper describes an automated approach to generating abstractions for the Tower of Hanoi and analyzes the use of these abstractions for problem solving. The analysis shows that the learned abstractions produce an exponential reduction in the size of the search space. Since few problem solvers actually explore the entire search space, the paper also presents an empirical analysis of the speedup provided by abstraction when a heuristic search is employed. The empirical analysis shows that the bene t of abstraction is largely determined by the portion of the base-level search space explored. Thus, using breadthrst search, which searches the entire space, abstraction provides an exponential reduction in search. However, using a depthrst search, the search reduction is smaller and depends on the amount of backtracking required to solve the problem. Abstractions, 1990