2014/04/15 by Guy Van den Broeck, Adnan Darwiche, Broeck, Guy Van den +1 · 1 citation
Computer Science · #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Formal Methods in Verification #Logic, Reasoning, and Knowledge #cs.AI
paper · pdf · doi:10.48550/arxiv.1404.4089
arxiv created 2014/04/15 · openalex publication_date 2014/04/15 · arxiv updated 2014/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of bottom-up compilation of knowledge bases, which is usually predicated on the existence of a polytime function for combining compilations using Boolean operators (usually called an Apply function). While such a polytime Apply function is known to exist for certain languages (e.g., OBDDs) and not exist for others (e.g., DNNF), its existence for certain languages remains unknown. Among the latter is the recently introduced language of Sentential Decision Diagrams (SDDs), for which a polytime Apply function exists for unreduced SDDs, but remains unknown for reduced ones (i.e. canonical SDDs). We resolve this open question in this paper and consider some of its theoretical and practical implications. Some of the findings we report question the common wisdom on the relationship between bottom-up compilation, language canonicity and the complexity of the Apply function.