Variable Shift SDD: A More Succinct Sentential Decision Diagram
This work provides a more efficient data structure for Boolean function representation, particularly benefiting domains like classical planning where symmetry exists, but it is incremental as it builds on existing SDD frameworks.
The authors tackled the problem of representing Boolean functions more succinctly by proposing Variable Shift SDD (VS-SDD), a variant of Sentential Decision Diagrams (SDDs), and showed that VS-SDDs can be exponentially smaller than SDDs while maintaining polynomial-time support for basic operations.
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.