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arXiv · 2407.17951

Pruning Boolean d-DNNF Circuits Through Tseitin-Awareness

Vincent Derkinderen
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Abstract

Boolean circuits in d-DNNF form enable tractable probabilistic inference. However, as a key insight of this work, we show that commonly used d-DNNF compilation approaches introduce irrelevant subcircuits. We call these subcircuits Tseitin artifacts, as they are introduced due to the Tseitin transformation step -- a well-established procedure to transform any circuit into the CNF format required by several d-DNNF knowledge compilers. We discuss how to detect and remove both Tseitin variables and Tseitin artifacts, leading to more succinct circuits. We empirically observe an average size reduction of 77.5% when removing both Tseitin variables and artifacts. The additional pruning of Tseitin artifacts reduces the size by 22.2% on average. This significantly improves downstream tasks that benefit from a more succinct circuit, e.g., probabilistic inference tasks.

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Vincent Derkinderen. 2024-07-25. Pruning Boolean d-DNNF Circuits Through Tseitin-Awareness. https://arxiv.org/abs/2407.17951

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