# On maximal QROBDD's of Boolean functions

Jean-Francis Michon; Jean-Baptiste Yunès; Pierre Valarcher

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 39, Issue: 4, page 677-686
- ISSN: 0988-3754

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topMichon, Jean-Francis, Yunès, Jean-Baptiste, and Valarcher, Pierre. "On maximal QROBDD's of Boolean functions." RAIRO - Theoretical Informatics and Applications 39.4 (2010): 677-686. <http://eudml.org/doc/92784>.

@article{Michon2010,

abstract = {
We investigate the structure of “worst-case” quasi reduced ordered decision diagrams and Boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity which leads to the concept of “hard” Boolean functions as functions whose QROBDD are “worst-case” ones. So we exhibit the relation between hard functions and the Storage Access function (also known as Multiplexer).
},

author = {Michon, Jean-Francis, Yunès, Jean-Baptiste, Valarcher, Pierre},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Boolean functions; Boolean complexity; Boolean graphs; binary decision diagrams; BDD; OBDD},

language = {eng},

month = {3},

number = {4},

pages = {677-686},

publisher = {EDP Sciences},

title = {On maximal QROBDD's of Boolean functions},

url = {http://eudml.org/doc/92784},

volume = {39},

year = {2010},

}

TY - JOUR

AU - Michon, Jean-Francis

AU - Yunès, Jean-Baptiste

AU - Valarcher, Pierre

TI - On maximal QROBDD's of Boolean functions

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 39

IS - 4

SP - 677

EP - 686

AB -
We investigate the structure of “worst-case” quasi reduced ordered decision diagrams and Boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity which leads to the concept of “hard” Boolean functions as functions whose QROBDD are “worst-case” ones. So we exhibit the relation between hard functions and the Storage Access function (also known as Multiplexer).

LA - eng

KW - Boolean functions; Boolean complexity; Boolean graphs; binary decision diagrams; BDD; OBDD

UR - http://eudml.org/doc/92784

ER -

## References

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- J.F. Michon, P. Valarcher and J.B. Yunès, Integer sequence number a100344. stored in The On-Line Encyclopedia of Integer Sequence, N.J.A. Sloane, published electronically at (2004). URIhttp://www.research.att.com/~njas/sequences
- W. Paul, A 2.5n lower bound on the combinatorial complexity of boolean functions. SIAM J. Comput.6 (1977) 427–443. Zbl0358.68081
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