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Variable Shift SDD: A More Succinct Sentential Decision Diagram

Authors Kengo Nakamura , Shuhei Denzumi , Masaaki Nishino

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Author Details

Kengo Nakamura
  • NTT Communication Science Laboratories, Kyoto, Japan
Shuhei Denzumi
  • Graduate School of Information Science and Technology, The University of Tokyo, Japan
Masaaki Nishino
  • NTT Communication Science Laboratories, Kyoto, Japan

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Kengo Nakamura, Shuhei Denzumi, and Masaaki Nishino. Variable Shift SDD: A More Succinct Sentential Decision Diagram. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 22:1-22:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


The Sentential Decision Diagram (SDD) is a tractable representation of Boolean functions that subsumes the famous Ordered Binary Decision Diagram (OBDD) as a strict subset. SDDs are attracting much attention because they are more succinct than OBDDs, as well as having canonical forms and supporting many useful queries and transformations such as model counting and Apply operation. In this paper, we propose a more succinct variant of SDD named Variable Shift SDD (VS-SDD). The key idea is to create a unique representation for Boolean functions that are equivalent under a specific variable substitution. We show that VS-SDDs are never larger than SDDs and there are cases in which the size of a VS-SDD is exponentially smaller than that of an SDD. Moreover, despite such succinctness, we show that numerous basic operations that are supported in polytime with SDD are also supported in polytime with VS-SDD. Experiments confirm that VS-SDDs are significantly more succinct than SDDs when applied to classical planning instances, where inherent symmetry exists.

Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
  • Computing methodologies → Knowledge representation and reasoning
  • Boolean function
  • Data structure
  • Sentential decision diagram


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