Characterizing the Complexity of Boolean Functions represented by Well-Structured Graph-Driven Parity-FBDDs

Henrik Brosenne; Matthias Homeister; Stephan Waack

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 36, Issue: 3, page 229-247
  • ISSN: 0988-3754

Abstract

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We investigate well-structured graph-driven parity-FBDDs, which strictly generalize the two well-known models parity OBDDs and well-structured graph-driven FBDDs. The first main result is a characterization of the complexity of Boolean functions represented by well-structured graph-driven parity-FBDDs in terms of invariants of the function represented and the graph-ordering used. As a consequence, we derive a lower bound criterion and prove an exponential lower bound for certain linear code functions. The second main result of this paper is a polynomial time algorithm that minimizes the number of nodes in a graph-driven parity-FBDD.

How to cite

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Brosenne, Henrik, Homeister, Matthias, and Waack, Stephan. "Characterizing the Complexity of Boolean Functions represented by Well-Structured Graph-Driven Parity-FBDDs." RAIRO - Theoretical Informatics and Applications 36.3 (2010): 229-247. <http://eudml.org/doc/92699>.

@article{Brosenne2010,
abstract = { We investigate well-structured graph-driven parity-FBDDs, which strictly generalize the two well-known models parity OBDDs and well-structured graph-driven FBDDs. The first main result is a characterization of the complexity of Boolean functions represented by well-structured graph-driven parity-FBDDs in terms of invariants of the function represented and the graph-ordering used. As a consequence, we derive a lower bound criterion and prove an exponential lower bound for certain linear code functions. The second main result of this paper is a polynomial time algorithm that minimizes the number of nodes in a graph-driven parity-FBDD. },
author = {Brosenne, Henrik, Homeister, Matthias, Waack, Stephan},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Well-structured graph-driven parity-FBDDs; lower bounds; minimization algorithm; complexity theory; data structures for Boolean functions.; polynomial time algorithm},
language = {eng},
month = {3},
number = {3},
pages = {229-247},
publisher = {EDP Sciences},
title = {Characterizing the Complexity of Boolean Functions represented by Well-Structured Graph-Driven Parity-FBDDs},
url = {http://eudml.org/doc/92699},
volume = {36},
year = {2010},
}

TY - JOUR
AU - Brosenne, Henrik
AU - Homeister, Matthias
AU - Waack, Stephan
TI - Characterizing the Complexity of Boolean Functions represented by Well-Structured Graph-Driven Parity-FBDDs
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 36
IS - 3
SP - 229
EP - 247
AB - We investigate well-structured graph-driven parity-FBDDs, which strictly generalize the two well-known models parity OBDDs and well-structured graph-driven FBDDs. The first main result is a characterization of the complexity of Boolean functions represented by well-structured graph-driven parity-FBDDs in terms of invariants of the function represented and the graph-ordering used. As a consequence, we derive a lower bound criterion and prove an exponential lower bound for certain linear code functions. The second main result of this paper is a polynomial time algorithm that minimizes the number of nodes in a graph-driven parity-FBDD.
LA - eng
KW - Well-structured graph-driven parity-FBDDs; lower bounds; minimization algorithm; complexity theory; data structures for Boolean functions.; polynomial time algorithm
UR - http://eudml.org/doc/92699
ER -

References

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  12. E.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes. Elsevier (1977).  Zbl0369.94008
  13. D. Sieling, Lower bounds for linear transformed OBDDs and FBDDs, in Proc. 19th FSTTCS. Springer Verlag, Lecture Notes in Comput. Sci.1738 (1999) 356-368.  Zbl0958.68071
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  15. St. Waack, On the descriptive and algorithmic power of parity ordered binary decision diagrams. Inform. Comput.166 (2001) 61-70.  Zbl1003.68049
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