# 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

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topBrosenne, 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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