Cause-effect graph to decision table example
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 |