# Cause-effect graph to decision table example

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Consider the boolean graph below:

Considering the causes, represented by the nodes 1, 2, 3 and 4, all the possible input conditions are:

Cause 1 Cause 2 Cause 3 Cause 4
0 0 0 0
0 0 0 1
0 0 1 0
0 0 1 1
0 1 0 0
0 1 0 1
0 1 1 0
1 0 0 0
1 0 0 1
1 0 1 0
1 1 0 0
1 1 0 1
1 1 1 0

However, some of the input condition does not are required to obtain all the possible valid results:

• Consider the nodes 5 and 6. Three input conditions results in (5,6) = (0,0): (0,0,0,0), (0,0,0,1) and (0,0,0,1), but just one of this conditions is actually required (e.g., (0,0,0,0)).
• Consider the nodes 5 and 6, respectively assigned the values 1 and 0. There is only one condition where 5 = 1 is required. Although the nodes (1,2,3,4) can be configured as (1,0,*,*), (0,1,*,*) and (1,1,*,*) so that the node 5 be 1, only one of these configurations is required. Thus, only one of these configurations is required. However, one of the cause-effect graph conditions states that, in an OR-type node, the inputs should not be assigned the value 1 all at the same time. So, we must select one of (1,0,*,*) and (0,1,*,*) for the nodes (1,2,3,4) configuration. Let's use the configuration (1,0,*,*). The configurations (0,1,*,*) and (1,1,*,*) must be eliminated.
• Consider the nodes 5 and 6 set to 0 and 1. There is only one condition where 6 = 1 is required: (0, 0, 1, 1).

The resulting decision table is:

Cause 1 Cause 2 Cause 3 Cause 4
0 0 0 0
0 0 1 1
1 0 0 0
1 0 0 1
1 0 1 0