Binary Decision Diagrams [Bryant]

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Binary Decision Diagrams Bryant

• Ordered decision tree for f a ? b ? c ? d

a
0
1
b
b
0
1
0
1
c
c
c
c
0
1
0
1
0
1
0
1
d
d
d
d
d
d
d
d
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OBDD reduction

• f a ? b ? c ? d

a
0
1
b
b
1
1
0
0
c
c
1
1
0
0
d
d
1
1
0
0
0
1
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OBDD properties

• Variable order strongly affects size
• Canonical representation for a given order
• Efficient apply algorithm
• boolean operations on BDDs is easy
• Can build BDDs for large circuits

f
fg
g
O(f g)
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Boolean quantification

• If v is a boolean variable, then
• v.f f v 0 f v 1
• Example (b,c). (ab ce bd) a e
  d
• Complexity on BDD representation
• worst case exponential
• heuristically efficient

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Characterizing Relations

• Represent any P Í 0,1n by its
  characteristic function cP
• P (v1,v2,,vn) cP
• Example
• Variables (x,y,z)
• P (0,0,1) , (0,1,0), (1,0,0), (1,1,1)
• cP x y z

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