Pruning Boolean d-DNNF Circuits Through Tseitin-Awareness

TL;DR

This paper identifies and removes Tseitin artifacts in d-DNNF circuits, significantly reducing circuit size and improving the efficiency of probabilistic inference tasks.

Contribution

It introduces methods to detect and eliminate Tseitin artifacts, leading to more compact d-DNNF circuits and enhanced inference performance.

Findings

Average size reduction of 77.5% after removing Tseitin variables and artifacts.

Additional 22.2% size reduction by pruning Tseitin artifacts.

Improved efficiency in probabilistic inference tasks.

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.