OBDDs, SDDs, and circuits of bounded width: Completeness matters

Abstract

Ordered Binary Decision Diagrams (OBDDs) are dynamic data structures with many application areas. The literature suggested that OBDDs of bounded width equate to Boolean circuits of bounded pathwidth. In this paper, we show that this relationship holds only for complete OBDDs. Additionally, we demonstrate that similar limitations affect the claimed equivalence between Sentential Decision Diagrams (SDDs) of bounded width and Boolean circuits of bounded treewidth.

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Item Type:	Article
Authors/Creators:	de Colnet, A. Ordyniak, S. https://orcid.org/0000-0003-1935-651X Szeider, S.
Copyright, Publisher and Additional Information:	/© 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Dates:	Accepted: 18 November 2025 Published (online): 30 November 2025 Published: February 2026
Institution:	The University of Leeds
Academic Units:	The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds)
Funding Information:	Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/V00252X/1
Date Deposited:	21 Nov 2025 11:45
Last Modified:	22 Apr 2026 11:55
Status:	Published
Publisher:	Elsevier
Identification Number:	10.1016/j.artint.2025.104458
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:234745

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OBDDs, SDDs, and circuits of bounded width: Completeness matters

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