Discrete integration is a fundamental problem in artificial intelligence, with applications in probabilistic reasoning, planning, inexact computing, engineering reliability, and statistical physics. The task is to count the total weight, subject to a given weight function, of the set of solutions of input constraints. The development of tools to compute the total weight on large industrial formulas is an area of active research.

Over the last ten years, hundreds of thousands of research hours have been poured into low-level computational tools and compilers for neural network training and inference. Simultaneously, there has been a surge in high-level reasoning tools based on graph decompositions, spurred by several competitions. While some existing discrete integration tools (counters) tightly integrate with these low-level computational or high-level reasoning tools, no existing counter is able to leverage both together.

In this thesis, we demonstrate that a clean separation of high-level reasoning (planning) and low-level computation (execution) leads to scalable and more flexible counters. Instead of building tightly on any particular tool, we target APIs that can be fulfilled by multiple implementations. This requires novel theoretical and algorithmic techniques to use existing high-level reasoning tools in a way consistent with the options available in popular low-level computational libraries. The resulting counters perform well in many hardware settings (singlecore, multicore, GPU).