Boolean Algebra for CAD Applications

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Presentation transcript:

Boolean Algebra for CAD Applications Shmuel Wimer Bar Ilan Univ., School of Engineering

Binary Decision Diagram – BDD Set one variable at a each level of tree Index=1 Index=2 Index=3 Evaluate function at leaves BDD OBDD b a 1 c a 1 c 1 1 b 1 1

Binary Decision Diagram – OBDD

OBDD Isomorphism and Redundancy

Reduced OBDD – ROBDD 1 b a c OBDD b a 1 c ROBDD

Bottom-up ROBDD Generation

1 b a c OBDD ROBDD a b 1 c 1 <4,3> Id=5 Id=5 <1,3> Id=4 b a c OBDD ROBDD <4,3> Id=5 a 1 Id=5 <1,3> Id=4 <3,3> Id=3 b 1 Id=4 <1,2> Id=3 <1,2> Id=3 1 c Id=3 1 Id=1 Id=2 Id=1 Id=2

ROBDD Construction with ITE Operator Instead of reducing OBDD, ROBDD can be constructed

a: 1 a b: 1 b c: 1 c 1 c ac+bc: b a 1 c ac: a 1 c bc: b

ITE Algorithm

ITE Applications