Logical Circuit Filtering

Dafna Shahaf, Eyal Amir

Logical Filtering is the problem of tracking the possible states of a world (belief state) after a sequence of actions and observations. It is fundamental to applications in partially observable dynamic domains. This paper presents the first exact logical filtering algorithm that is tractable for all deterministic domains. Our tractability result is interesting because it contrasts sharply with intractability results for structured stochastic domains. The key to this advance lies in using logical circuits to represent belief states. We prove that both filtering time and representation size are linear in the sequence length and the input size. They are independent of the domain size if the actions have compact representations. The number of variables in the resulting formula is at most the number of state features. We also report on a reasoning algorithm (answering propositional questions) for our circuits, which can handle questions about past time steps (smoothing). We evaluate our algorithms extensively on AI-planning domains. Our method outperforms competing methods, sometimes by orders of magnitude.