Hardware Reference
In-Depth Information
corresponding to Fig.
2.1
b is shown in Fig.
2.15
c. When the error is detected in the
output of Mix 3 at time 10, the ongoing operation Mix 1 is executed based on the
initial synthesis result. We assume that the computing time of generating the new
synthesis result is 1 time slot. In practice, the computation time is at least an order of
magnitude less than the operation time of fluid-handing operations. Then at time 11,
the control software will generate re-synthesis result based on the updated Fig.
2.1
b.
As shown in Fig.
2.15
c, Mix 1 is completed at time 12 without being interrupted.
The experiment is finished at time 18. Thus the bioassay is executed “seamlessly”
without any time penalty or interruption of other operations.
The re-synthesis problem can also be solved using the PRSA-based global
optimization method from [
1
]. The inputs and constraints of the re-synthesis
problem are different from the initial synthesis problem introduced in Sect.
2.3.1
.
Suppose the set of operations for the re-synthesis problem is
P
0
and the set
C
0
. We can derive
P
0
and
C
0
based on
of constraints is
P
and
C
introduced
in Sect.
2.3
.
We first define an operator
is a mapping from the set of all
operations to the set of operations that have already started at time instant t .
T
on the set
P
.
T
.t /
Df
op t
i
j
M
opt
i
.1/
t
g
T
.t /
W
P
!
P
When an error is detected at time instant t in operation
opt
i
, the set of operations
that need to be re-synthesized can be written as
Q
P
0
D
P
[
R
i
[
O
P
.t /.
Here
R
i
is the set of recovery operations corresponding to erroneous operation
opt
i
,and
Q
is the set of subsequently operations which will be implemented on
electrodes with defect in the initial synthesis result. The method for determining the
operations in
O
R
i
is introduced in Sect.
2.4.1
. Then based on the module placement
information included in initial synthesis result, and locations of electrodes with
defects, operations in
Q
can be determined.
We write the new synthesis results for
opt
i
2
O
P
0
as M
opt
i
. In addition to the set
of constraints
, the re-synthesis result must satisfy the constraint that: the region
where an error has been deemed to have occurred, cannot be used any more.
The optimization problem for re-synthesis process can be written as:
C
f
M
opt
i
.2/
g
minimize: Max
opt
i
2
P
0
The above optimization problem can be solved by using the PRSA-based synthesis
procedure introduced in [
1
]. Using this method, we can derive globally-optimized
synthesis results with short assay completion time, while the CPU time is in the
order of 20 min for a typical bioassay [
11
]. Thus, this method is not suitable for
on-line computation of re-synthesis results.
