The name is absent



The number of measurements also affects the estimation error. Figure 6.3
presents variation estimation error versus number of measurements. The hori-
zontal axis is the ratio of measurements to the total number of the gates in the
circuit. The variation is estimated on 7V∕4-dimensional subspace.
M is 383 and
317 for C499 and C880 respectively
(M denotes the number of measurements in
Table 6.2). Note that as the number of measurements increases, they cover most
of the identifiable directions. Thus sparsity and shape constraints are similar in
large number of measurements and the errors of the ^ɪ-regularization and TUSC
become nearly the same.

Table 6.1 shows average number of the independent power vectors for single
and multiple voltage measurement. The second column is the number of power
vectors (measurements). To find number of the independent vectors in each mea-
surement set, we first find their singular values, then we count the number of
non-zero singular values. The third and fifth columns show the number of inde-
pendent power vectors for single and triple voltage measurements, respectively.
The table explains that triple voltage measurements increases the number of
independent power vectors.

Table 6.2 shows tomography results on different benchmark circuits. We used
the software package SIS [67] with NAND2, NAND3, NAND4, N0R2, N0R3,
N0R4, and inverters to map the circuit to the logic gates. The second column
shows the number of gates and the third column reports the number of input

71



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