File:BDD Variable Ordering VisuBDD Bad.png

The PNG picture is 518 x 32 pixel.

Other BDD pictures for similar formulas:

• 
  BDD graph for the Boolean formula x1 * x2 + x3 * x4 + x5 * x6 + x7 * x8 using a good variable ordering
• 
  BDD graph for the Boolean formula x1 * x2 + x3 * x4 + x5 * x6 + x7 * x8 using a bad variable ordering

The following is the RML (Relational Manipulation Language) code that I fed to CrocoPat to produce the dat files for VisuBDD:

// RML program to generate BDD visualizations for the formula
// x1 & x2 | x3 & x4 | ... | x19 & x20,
// using two different variable orderings.
// "crocopat -e BDD_Variable_Ordering_VisuBDD.rml" 
// generates two files in dat format.
// "java -classpath <your_CrocoPat_dir> 
//  VisuBDD.VisualizeSize  BDD_Variable_Ordering_VisuBDD_Bad.dat"
// displays a visualization of the BDD graph on screen.

// There are two ('Boolean') values for the variables x1, ..., x20.
DOM("0");
DOM("1");

// F is the name of the Boolean formula.
F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20) := 
                               (x1="1" & x2="1") 
                             | (x3="1" & x4="1")
                             | (x5="1" & x6="1")
                             | (x7="1" & x8="1")
                             | (x9="1" & x10="1") 
                             | (x11="1" & x12="1")
                             | (x13="1" & x14="1")
                             | (x15="1" & x16="1")
                             | (x17="1" & x18="1")
                             | (x19="1" & x20="1");

// Prints the number of nodes per variable in dat format for VisuBDD,
// using a good variable ordering resulting in linear size of the graph.
PRINT NODESPERVAR( F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20) ) 
      TO "BDD_Variable_Ordering_VisuBDD_Good.dat";

// Prints the number of nodes per variable in dat format for VisuBDD,
// using a bad variable ordering resulting in exponential size of the graph.
// The first term of the conjunction sets the variable ordering.
PRINT NODESPERVAR( TRUE(x1,x3,x5,x7,x9,x11,x13,x15,x17,x19,x2,x4,x6,x8,x10,x12,x14,x16,x18,x20) &
                   F(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20) ) 
      TO "BDD_Variable_Ordering_VisuBDD_Bad.dat";;

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• share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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