Abstract
In this chapter we analyze the influence of the variable order on the complexity of OBDDs. The following two theorems, which immediately follow from the Theorems and Corollaries 6.9 to 6.12, are applied several times.
Alle Räder stechen still, wenn dein starker Arm es will. [All wheels stand still if your strong arm o will.] Georg Herwegh (1817–1875)
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References
The asymptotic statements about switching functions go back to Shannon [Sha49]. The mentioned paper concerning a linear lower bound for circuits is by Blum [B1u84]. The proofs of the exponential lower bounds of multiplication as well as for the hidden weighted bit function can be found in [Bry91]. Our treatment follows the presentation of Ponzio [Pon95].
The polynomial algorithm for performing the equivalence test of OBDDs with different orders was designed by Fortune, Hoperoft, and Schmidt [FHS78]. Gergov and Meinel proved that performing binary operations on OBDDs with different orders is NP-hard [GM94b]. Efficient algorithms for global rebuilding were designed independently by Meinel and Slobodová [MS94], by Savickÿ and Wegener [SW97], and by Tani and Imai [TI94].
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© 1998 Springer-Verlag Berlin Heidelberg
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Meinel, C., Theobald, T. (1998). Influence of the Variable Order on the Complexity of OBDDs. In: Algorithms and Data Structures in VLSI Design. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58940-9_8
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DOI: https://doi.org/10.1007/978-3-642-58940-9_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64486-6
Online ISBN: 978-3-642-58940-9
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