Difference between revisions of "Binary decision diagram"
From ScienceZero
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# Merge equivalent leaves - We want two leaves, [ 1 ] and [ 0 ]. Redirect all edges from the removed nodes to the equivalent leave | # Merge equivalent leaves - We want two leaves, [ 1 ] and [ 0 ]. Redirect all edges from the removed nodes to the equivalent leave | ||
# Merge isomorphic nodes - Remove all nodes that have the same variable and identical children as another node. Redirect all edges that went into the redundant node into the one copy that you kept | # Merge isomorphic nodes - Remove all nodes that have the same variable and identical children as another node. Redirect all edges that went into the redundant node into the one copy that you kept | ||
− | # Eliminate | + | # Eliminate redundant tests - Remove all nodes that has the same child twice. Redirect all edges into redundant node into the child node |
# Repeat steps 4 5 6 until no more improvements can be made | # Repeat steps 4 5 6 until no more improvements can be made | ||
− | We now have a canonical reduced ordered binary decision diagram. All nodes represents different functions that all are canonical. | + | We now have a canonical reduced ordered binary decision diagram. All nodes now represents different functions that all are canonical. |
'''Problem:''' This procedure becomes impossible with more than 5 variables. With 6 variables the truth table alone will be 2^64 bits long! | '''Problem:''' This procedure becomes impossible with more than 5 variables. With 6 variables the truth table alone will be 2^64 bits long! |
Revision as of 16:43, 6 May 2014
- Decider order of variables
- Create truth table
- Create tree from truth table
- Merge equivalent leaves - We want two leaves, [ 1 ] and [ 0 ]. Redirect all edges from the removed nodes to the equivalent leave
- Merge isomorphic nodes - Remove all nodes that have the same variable and identical children as another node. Redirect all edges that went into the redundant node into the one copy that you kept
- Eliminate redundant tests - Remove all nodes that has the same child twice. Redirect all edges into redundant node into the child node
- Repeat steps 4 5 6 until no more improvements can be made
We now have a canonical reduced ordered binary decision diagram. All nodes now represents different functions that all are canonical.
Problem: This procedure becomes impossible with more than 5 variables. With 6 variables the truth table alone will be 2^64 bits long!
Solution: Build the reduced tree directly from the boolean expression.
How: To be determined...