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Belief tracking is a basic problem in planning with sensing. While theproblem is intractable, it has been recently shown that for both deterministicand non-deterministic systems expressed in compact form, it can be done in timeand space that are exponential in the problem width. The width measures themaximum number of state variables that are all relevant to a given preconditionor goal. In this work, we extend this result both theoretically andpractically. First, we introduce an alternative decomposition scheme andalgorithm with the same time complexity but different completeness guarantees,whose space complexity is much smaller: exponential in the causal width of theproblem that measures the number of state variables that are causally relevantto a given precondition, goal, or observable. Second, we introduce a fast,meaningful, and powerful approximation that trades completeness by speed, andis both time and space exponential in the problem causal width. It is thenshown empirically that the algorithm combined with simple heuristics yieldsstate-of-the-art real-time performance in domains with high widths but lowcausal widths such as Minesweeper, Battleship, and Wumpus.

Causal Belief Decomposition for Planning with Sensing: Completeness Results and Practical Approximation