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Explore a 15-minute conference presentation examining the theoretical relationship between Binary Decision Diagrams (BDDs) and Context-Free-Language Ordered Decision Diagrams (CFLOBDDs) in Boolean function representation. Learn how researchers Xusheng Zhi and Thomas Reps from the University of Wisconsin-Madison address a fundamental open question in computational complexity by establishing polynomial bounds between these two data structures. Discover their proof that CFLOBDDs using the same variable ordering as corresponding BDDs cannot be exponentially larger, with the CFLOBDD size bounded by O(n³) where n is the BDD size. Understand the significance of this worst-case analysis, which demonstrates that while CFLOBDDs can be exponentially more succinct than BDDs in best-case scenarios, they maintain polynomial overhead in worst-case situations. Examine the tightness of these bounds through concrete function families where the cubic relationship is achieved, providing complete characterization of the size relationship between these important Boolean function representation methods used in formal verification and symbolic computation.
