In the past one week I rewrote the ISLPED submission, made changes according to the review comments of DAC and ISLPED, and submitted the paper to ICCD. Meanwhile I search the literature for current studies on voltage scaling. I find out that although there has been extensive studies on voltage scaling with discrete vdd levels, all of them (as far as I have read) focus on the scheduling algorithm assuming (1) the number of discrete vdd levels are fixed; and (2) the value for each vdd level are given. What we are going to study differs from them in the sense that our goal is to fix the number of Vdd levels and the value of each level. Our problem can be: given the characteristics of a task set (distribution of execution time), decide the design of voltage scaling circuit with N discrete vdd levels, such that total power can be minimized under given QoS. There are some starting points we can take. Without considering leakage power, first, it has been proved that for each task with its execution time, there is one optimal Vdd for minimum power while meeting the deadline. Second, with discrete voltage levels, at most two vdd levels are enough for one task with a deadline to achieve minimum power. With leakage power these conclusion may change, which we can try. I feel these two conclusions may be helpful in our problem solving and I am still try to make the problem more clear.