Exercise 4

Figure A.5

Is this a valid logic flow circuit? Yes.

There are five linearly independent paths possible through this system.

Figure A.6

However, these five paths can be covered in four traversals. If the order in which the nodes are covered is not important, then Path 4 is not necessary. All the path segments that it covers are covered in the other four traversals. There are a total of six different ways to traverse the five linearly independent paths that exist in this system.

Figure A.7

Note 

Calculating the number of IPs does not tell where the paths are in the system, only how many exist.

The number of linearly independent paths is not always the minimum number of traversals required to cover all path segments one time. However, it requires detailed analysis to determine whether or not a system can be covered in fewer than the calculated number of linearly independent paths. For the purpose of estimating the number of path traversals that will be traversed as a minimum, the number of linearly independent paths is still an excellent metric.

Figure A.8