We propose a novel concise function representation for graphical models, a central theoretical framework that provides the basis for many reasoning tasks. We then show how we exploit our concise representation based on deterministic finite state automata within Bucket Elimination (BE), a general approach based on the concept of variable elimination that accommodates many inference and optimisation tasks such as most probable explanation and constrained optimisation. We denote our version of BE as FABE. By using our concise representation within FABE, we dramatically improve the performance of BE in terms of runtime and memory requirements. Results on standard benchmarks obtained using an established experimental methodology show that FABE often outperforms the best available approach (RBFAOO), leading to significant runtime improvements (up to 2 orders of magnitude in our tests).
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