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Binary Decision Diagrams (BDD)

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What are they?

• BDDs are an advanced form of a binary tree

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Binary Tree Representation of Boolean Function

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How does a BDD remedy this memory problem?

• BDDs use reduction process in order to

eliminate redundant nodes and terminals.

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Decision Structures  Vertex represents decision  Follow green (dashed) line for value 0  Follow red (solid) line for value 1  Function value determined by leaf value. Truth Table Decision Tree 0 0 x 3 0 1 x 3 x 2 0 1 x 3 0 1 x 3 x 2 x 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 x 1 x 2 x 3 f

Reduction Rule # Merge equivalent leaves a a 0 0 x 3 0 1 x 3 x 2 0 1 x 3 0 1 x 3 x 2 x 1 x 3 x 3 x 2 x 3 0 1 x 3 x 2 x 1 a

Reduction Rule # x 3 x 2 0 1 x 3 x 2 x 1 Eliminate Redundant Tests y x y x 2 0 1 x 3 x 1

Example BDD Initial Graph Reduced Graph x 2 0 1 x 3 x 1 0 0 x 3 0 1 x 3 x 2 0 1 x 3 0 1 x 3 x 2 x 1 (x1+x2)x

Binary Decision Diagrams

• Graphical encoding of a truth table. 13 x x x3 x x4 x4 x 0 0 0 1 0 0 0 0 x x x3 x x4 x4 x 0 1 1 1 0 0 0 1 x1 0 edge 1 edge

Binary Decision Diagrams

• Collapse redundant nodes. 14 x x x3 x x4 x4 x 0 0 0 0 0 0 0 x x x3 x x4 x4 x 0 0 0 0 x 1 1 1 1 1

Binary Decision Diagrams

• Collapse redundant nodes. 16 x x x3 x x x3 x x4 x 0 x 1

Binary Decision Diagrams

• Collapse redundant nodes. 17 x x x3 x x x x4 x 0 x 1

Binary Decision Diagrams

• Eliminate unnecessary nodes. 19 x x x x x 0 x 1

Yoga BABY!!!

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