New Compilation Languages Based on Restricted Weak Decomposability

This paper introduces two new compilation languages restricting weak decomposable negation normal form (wDNNF) circuits and integrates them into the knowledge compilation map. Positive (resp. negative) wDNNF circuits restrict wDNNF circuits so that each variable shared among the inputs of a conjunction node can only have positive (resp. negative) occurrences in that subcircuit. Unlike wDNNF circuits, pwDNNF (resp. nwDNNF) circuits satisfy the maximum (resp. minimum) cardinality query. We present a compiler for converting CNF formulae into pwDNNF and nwDNNF circuits by extending Bella - the state-of-the-art compiler for wDNNF circuits. We introduce a new caching scheme, called Cara, that exploits isomorphism. Using that scheme, we show a new compilation method based on copying subcircuits, which may significantly speed up compilations at the expense of increasing circuit sizes. Our experiments demonstrate that nwDNNF circuits are suitable for computing most probable explanations (MPEs) in two-layer Bayesian networks (BNs) with large domains.