We present and evaluate a new compiler, called d4, targeting the Decision-DNNF language. As the state-of-the-art compilers C2D and Dsharp targeting the same language, d4 is a top-down tree-search algorithm exploring the space of propositional interpretations. d4 is based on the same ingredients as those considered in C2D and Dsharp (mainly, disjoint component analysis, conflict analysis and non-chronological backtracking, component caching). d4 takes advantage of a dynamic decomposition approach based on hypergraph partitioning, used sparingly. Some simplification rules are also used to minimize the time spent in the partitioning steps and to promote the quality of the decompositions. Experiments show that the compilation times and the sizes of the Decision-DNNF representations computed by d4 are in many cases significantly lower than the ones obtained by C2D and Dsharp.

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In this paper, we investigate the computational intelligibility of Boolean classifiers, characterized by their ability to answer XAI queries in polynomial time. The classifiers under consideration are decision trees, DNF formulae, decision lists, decision rules, tree ensembles, and Boolean neural nets. Using 9 XAI queries, including both explanation queries and verification queries, we show the existence of large intelligibility gap between the families of classifiers. On the one hand, all the 9 XAI queries are tractable for decision trees. On the other hand, none of them is tractable for DNF formulae, decision lists, random forests, boosted decision trees, Boolean multilayer perceptrons, and binarized neural networks.

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