A Distributed Framework for Compiling and Reasoning with d-DNNF

2026-07-15

AI Summary

This work addresses the challenge that large-scale propositional formulas, when compiled into deterministic Decomposable Negation Normal Form (d-DNNF), often exceed the memory and time limits of single-node systems, hindering efficient downstream inference. To overcome this limitation, the authors propose the first distributed framework for d-DNNF knowledge compilation and reasoning. Leveraging a Cube-and-Conquer strategy to partition the search space, they develop a distributed compiler, dkc, along with a companion inference engine, dreasoner, which supports tasks such as model counting, direct query answering, and uniform sampling. The framework introduces novel techniques to handle circuit fragment sharing and minimize communication overhead. Evaluated on standard benchmarks, it substantially extends the scale and complexity of formulas that can be compiled and queried, successfully processing instances beyond the reach of existing sequential tools.

Abstract

Knowledge Compilation (KC) is a powerful paradigm that enables efficient reasoning by transforming propositional formulas into tractable target languages, such as Deterministic, Decomposable Negation Normal Form (d-DNNF). However, as real-world problem instances grow in complexity, the offline compilation phase becomes a significant computational bottleneck, often exceeding the memory and temporal limits of single-node systems. While distributed computing has been successfully applied to model counting ($\#\mathsf{SAT}$), extending these techniques to knowledge compilation remains a challenge due to the difficulty of sharing partial circuit fragments across distributed nodes. In this paper, we propose dkc, the first distributed knowledge compiler designed for large-scale Decision-DNNF generation. Leveraging a Cube-and-Conquer strategy, dkc effectively partitions the search space into independent subproblems, mitigating the communication overhead typically associated with work-stealing architectures in circuit-based tasks. Recognizing that the utility of compilation lies in subsequent querying, we further introduce dreasoner, a distributed reasoning engine. dreasoner is capable of performing core inference tasks (including model counting, direct access, and uniform sampling) across a distributed d-DNNF structure, even under variable conditioning. Our experimental evaluation on benchmarks demonstrates that our distributed architecture scales effectively, enabling the compilation and querying of complex formulas that remain beyond the reach of state-of-the-art sequential compilers.

Problem

• Knowledge Compilation
• d-DNNF
• Distributed Computing
• Computational Bottleneck
• Circuit Sharing

Innovation

• distributed knowledge compilation
• d-DNNF
• Cube-and-Conquer
• model counting
• distributed reasoning