Exploiting Belief State Structure in Graph Search

It is well-known that eliminating repeated states is essential for efficient search of state-space AND-OR graphs. The same technique has been found useful for searching beliefstate AND-OR graphs, which arise in nondeterministic partially observable planning problems and in partially observable games. Whereas physical states are viewed by search algorithms as atomic and admit only equality tests, belief states, which are sets of possible physical states, have additional structure: one belief state can subsume or be subsumed by another. This paper presents new algorithms that exploit this property to achieve substantial speedups. The algorithms are demonstrated on Kriegspiel checkmate problems and on a partially observable vacuum world domain.