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

Published online by Cambridge University Press:  15 December 2002

Henrik Brosenne ,
Matthias Homeister  and
Stephan Waack
Henrik Brosenne
Affiliation:
Institut für Numerische und Angewandte Mathematik, Georg-August-Universität Göttingen, Lotzestr. 16-18, 37083 Göttingen, Germany; homeiste@math.uni-goettingen.de. waack@math.uni-goettingen.de.
Matthias Homeister
Affiliation:
Institut für Numerische und Angewandte Mathematik, Georg-August-Universität Göttingen, Lotzestr. 16-18, 37083 Göttingen, Germany; homeiste@math.uni-goettingen.de. waack@math.uni-goettingen.de.
Stephan Waack
Affiliation:
Institut für Numerische und Angewandte Mathematik, Georg-August-Universität Göttingen, Lotzestr. 16-18, 37083 Göttingen, Germany; homeiste@math.uni-goettingen.de. waack@math.uni-goettingen.de.
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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.

Keywords

Well-structured graph-driven parity-FBDDslower boundsminimization algorithmcomplexity theorydata structures for Boolean functions.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 36 , Issue 3 , July 2002 , pp. 229 - 247
Copyright
© EDP Sciences, 2002

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