Approximation Techniques for Space-Efficient Compilation in Abductive Inference

We address the problem of approximately compiling propositional abduction problems (PAPs). We show intractability of compiling a PAP into a fixed-size representation, and of compiling a PAP to within a factor ɛ> 0 of the compilation of minimal size. Although generating an approximate compilation is intractable in general, we describe a preference-based PAP for which order-of-magnitude smaller compilations can be generated. We show that by restricting the distribution of solutions of a boolean function f to be power-law or exponential, we can compile a representation that approximates the solution coverage within a factor ɛ> 0 yet requires ordersof-magnitude less space than that of complete compilations. We present empirical results for the compilation languages of DNNF and prime implicants.