Biomedical Engineering Reference
In-Depth Information
5.3.4
Implementation of Fault and Drug Simulation
5.3.4.1
Case 1: Single Stuck-at Fault Identification
In this method, we find all single stuck-at faults which are non-redundant, as well as
the faulty outputs that they generate. To proceed with this method, we first simulate
the original circuit to determine the correct fault-free output. The circuit is simulated
using our SAT formulation in the fault-free and drug-free model for specified primary
input values, and the resulting primary output values for the true response is saved
as
Z
0
.
The next step is to find all faults which are non-redundant. To avoid having to
do an exhaustive search on all single stuck-at faults, we perform an All-SAT on the
circuit
S
where we constrain the output to be not
Z
0
. Assuming
n
output signals, this
constraint is formed as the clause
C
1
shown in Eq.
5.1
.
C
1
=
(
Z
0
+
Z
1
+···
Z
n
)
(5.1)
Here
Z
i
is the variable corresponding to the
i
th
output bit.
Furthermore, we also add a constraint to
S
that the circuit contains only one fault
that is injected at a time. This second constraint
C
2
(Eq.
5.2
) is formed by writing
clauses of all pairwise combinations of faults, where
k
is the number of stuck-at
faults and
f
i
is the
i
th
fault.
C
2
=
(
f
1
+
f
2
)
·
(
f
1
+
f
3
)
···
(
f
k
−
1
+
f
k
)
(5.2)
We now form a new CNF
S
1
C
2
. The resulting All-SAT on
S
1
is a list of all
non-redundant single stuck-at faults and their faulty output. These faults are flagged
for drug simulation using any of the next three cases, as described in the following
sections.
The results from this case can also be used immediately in several ways. For ex-
ample, this method classifies for each single stuck-at fault whether it is redundant or
non-redundant. That is, any fault which is redundant does not produce an incorrect
output, and can be ignored from a therapy standpoint. In a second example, the faulty
output from the stuck-at model can be compared to a measured output from expres-
sion data, in order to identify which genes are potentially faulty. This information
can be used to target genes for potential drug development, avoiding genes that are
untestable.
C
1
=
S
·
·
5.3.4.2
Case 2: Fault Rectification with Fewest Drugs
In the presence of a particular fault, the problem is determining whether a selection
of drugs can rectify the circuit, i.e. change the faulty output to the correct output. If
this is not possible, we want to obtain the “best” or “closest” output (in a Hamming
distance sense) to the correct output, by using drugs. To do this, we guide the WPMS
