Summary

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";;

Licensing

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• to remix – to adapt the work

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• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
• 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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