Test Compaction

In a test generation process for a combinational circuit six tests, $t_1,t_2,t_3,t_4,t_5,t_6$ are

generated to cover a set of given faults. Later it is discovered that we are interested only

in a subset of the faults and the subset consists of eight faults, $f_1,f_2,f_3,f_4,f_5,f_6,f_7,f_8.$

Though simulating the six tests for each of the faults $($without fault dropping$)$ we find the

detection capability of each test as given below.

The test $t_1$ can detect faults $f_3$ and $f_5$

The test $t_2$ can detect faults $f_2$ and $f_7$

The test $t_3$ can detect faults $f_2,f_3,$ and $f_7$

The test $t_4$ can detect faults $f_1,f_2,$ and $f_7$

The test $t_5$ can detect faults $f_4,$ and $f_6$

The test $t_6$ can detect faults $f_1,f_4,f_6$ and $f_8$

$($a$)$

If a reverse order fault simulation method is used to reduce the test set,

what will be test set produced by such a method to detect all the eight faults? Assume

that the original test set order is $t1t2$dotst$6.$ Show your work but be brief.

$($b$)$ Find a smallest set of tests that can detect all eight faults. You must show

your work to prove that the set obtained by you is the smallest set.