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

Abstract

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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).

How to cite

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Michon, 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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  1. R.E. Bryant, Graph based algorithms for boolean function manipulation. IEEE Trans. Comput.C-35 (1986) 677–691.  Zbl0593.94022
  2. C. Gröpl, Binary Decision Diagrams for Random Boolean Functions. Ph.D. Thesis, Humboldt-Universität zu Berlin (1999).  
  3. C. Gröpl, H.J. Prömel and A. Srivastav, Size and structure of random ordered binary decision diagrams (extended abstract), in STACS'98, Springer Verlag. Lect. Notes Comput. Sci.1373 (1998) 238–248.  
  4. C. Gröpl, H.J. Prömel and A. Srivastav, On the evolution of the worst-case obdd size. Inform. Process. Lett.77 (2001) 1–7.  Zbl1003.68050
  5. M. Heap and M.R. Mercer, Least upper bounds on obdd sizes. IEEE Trans. Comput.43 (1994) 764–767.  Zbl1033.68682
  6. 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
  7. W. Paul, A 2.5n lower bound on the combinatorial complexity of boolean functions. SIAM J. Comput.6 (1977) 427–443.  Zbl0358.68081
  8. I. Wegener, The complexity of Boolean functions. Wiley (1987).  Zbl0623.94018
  9. I. Wegener, Branching programs and binary decision diagrams. SIAM Monogr. Discrete Math. Appl. (2000).  Zbl0956.68068

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