Do CFLOBDDs Actually Make Use of Linear Structure?

2026-05-14

AI Summary

This study investigates whether the Compact Function-Linear Ordered Binary Decision Diagram (CFLOBDD) truly relies on its linear structure—not merely its hierarchical organization—for achieving efficient compression of Boolean functions. Through formal modeling, complexity analysis, and quantum circuit simulation experiments, and by leveraging theoretical insights from Nested-Word Automata and Visibly Pushdown Automata, this work provides the first explicit demonstration of the critical role played by the linear structure in CFLOBDD’s compression capability. The findings reveal that the linear and hierarchical structures jointly enable compact representations; removing the linear structure leads to a substantial blowup in representation size and causes significant performance degradation in quantum circuit simulations.

Abstract

Binary Decision Diagrams (BDDs) are a widely used data structure for efficient Boolean function representation. Context-Free-Language Ordered Binary Decision Diagrams (CFLOBDDs) are a recently introduced hierarchical data structure that can, in the best case, exhibit exponential compression over BDDs and double-exponential compression over decision trees. Roughly speaking, a CFLOBDD is a finite, acyclic, non-recursive hierarchical finite-state machine (HFSM) (with some additional restrictions). In this paper, we investigate the role of \emph{linear structure} in CFLOBDDs -- a property that connects them to Nested-Word Automata (NWAs) and Visibly Pushdown Automata (VPAs) -- and examine whether CFLOBDDs actively exploit this structure beyond their well-studied hierarchical properties. We demonstrate that linear structure, in conjunction with hierarchical structure, plays a crucial role in enabling CFLOBDDs to achieve efficient function compression. Furthermore, we show that removing linearity from CFLOBDDs leads to a significant blowup in representation size, resulting in degraded performance in the domain of quantum-circuit simulation.

Problem

• CFLOBDDs
• linear structure
• hierarchical structure
• Boolean function compression
• representation size

Innovation

• CFLOBDD
• linear structure
• hierarchical representation
• function compression
• quantum-circuit simulation