Average and worst case number of nodes in decision diagrams of symmetric multiple-valued functions

Butler, Jon T.; Herscovici, David S.; Sasao, Tsutomu; Barton, R.J.

doi:10.1109/12.588065

Cited by 12 publications

(2 citation statements)

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“…Some works already deal with complexity issues of the partially symmetric Boolean functions [8] and the symmetric multivalued functions [6,11,12]. They show that decision diagrams [4,15] are well suited to benefit from symmetries and we enhance this further on with excellent results for symmetric multivalued functions.…”

Section: Introductionmentioning

confidence: 97%

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De Bruijn sequences and complexity of symmetric functions

Rovetta¹,

Mouffron²

2011

Cryptogr. Commun.

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A multivalued function is a function from a set E n q to a set E m , where E k is a set which contains k elements. These functions are used in cryptography: cipher design, hash function design and in theoretical computer science. In this paper, we study the representation of these functions with Multivalued Decision Diagrams (MDD). This representation can be used both to measure complexity and to implement efficiently the functions in hardware. We are especially interested in symmetric functions. We show that symmetric functions MDDs have much lower size than classical functions MDDs. One major result is to determine exactly their MDD's maximum size. Notably, we highlight the links between De Bruijn sequences and the most complex symmetric functions and new functions are exhibited in the case q = 2 and any m. Enumeration of these functions are supplied, they are shown to be sufficiently numerous to allow many applications.

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Section: Introductionmentioning

confidence: 97%

“…So, their study gives directly the best size of any MDD representation. Another asset of symmetric functions is that their MDD have bounds [6,12] of small order, but no result expresses exactly the maximum size. No result provides functions achieving this maximum either.…”

Section: Introductionmentioning

confidence: 99%