### Table 8. Number of different states using Nonlinear Elimination.

"... In PAGE 18: ... The observation should be made that the trend of changes remained constant for all three multiplication factors. Table8 shows that the biggest reduction in sensitivity was obtained when we used the Nonlinear Elimination algorithm. For 6R general and Puma manipulators the sensitivity to units was 4.... In PAGE 21: ... Now, solving this subsystem of equations is an attempt in orienting the manipulator in the work space without paying attention to positioning. A degree of success of such an approach is depicted in Table8 . The sensitivity to units for Puma manipulator was completely removed while for 6R general manipulator it was reduced to about ... ..."

### Table 2. Elimination lemmas

2004

"... In PAGE 3: ... Note that the de- pendency graph of the constructions must be cycle free. To eliminate a point from the goal we need to apply one of the elimination lem- mas shown on Table2 on page 5. This table can be read as follows: To eliminate a point Y , choose the line corresponding to the way Y has been constructed, and apply the formula given in the column corresponding to the geometric quantity in which Y is used.... In PAGE 4: ... We rst translate the goal (A0B0 k AB) into its equivalent using the signed area: SA0B0A = SA0B0B Then we eliminate compound points from the goal starting by the last point in the order of their construction. The geometric quantities containing an oc- currence of B0 are SA0B0B and SA0B0A, B0 has been constructed using the rst construction on Table2 with = 1 2: SA0B0A = SAA0B0 = 1 2SAA0A + 1 2SAA0C = 1 2SAA0C and SA0B0B = SBA0B0 = 1 2SBA0A + 1 2SBA0C The new goal is SAA0C = SBA0A + SBA0C Now we eliminate A0 using: SCAA0 = 1 2SCAB + 1 2SCAC = 1 2SCAB SABA0 = 1 2SABB + 1 2SABC = 1... In PAGE 11: ... This tactic (called eliminate_all) rst searches the con- text for a point which is not used to build another point (a leaf in the dependency graph). Then for each occurrence of the point in the goal, it applies the right lemma from Table2 by nding in the context how the point has been constructed and which geometric quantity it appears in. Finally it removes the hypotheses stating how the point has been constructed from the context.... In PAGE 12: ...this classical reasoning step. As noted before, the elimination lemmas given in Table2 on page 5, do eliminate an occurrence of a point Y only if Y appears only one time in the geometric quantity (A,B,C and D must be di erent from Y ). If Y appears twice in S, this is not a problem because then the geometric quantity is zero, and so already eliminated by the simpli cation phase.... ..."

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### Table 1: Heuristics implemented for each choice point

1999

"... In PAGE 5: .... temporal placement of the moved or added activity (i.e., start time and duration). In Table1 , we outline the heuristics implemented within DCAPS for each of these choice points (the heuristic method actually used is marked with an asterisk). After... ..."

Cited by 8

### Table 7.2: Percentage of dynamic instructions eliminated using the SLP heuristic for

2000

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### Table 7.3: Percentage of dynamic instructions eliminated using the SLP heuristic and

2000

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### Table 7.2: Percentage of dynamic instructions eliminated using the SLP heuristic for a variety of hypothetical datapath widths.

2000

### Table 7.2: Percentage of dynamic instructions eliminated using the SLP heuristic for a variety of hypothetical datapath widths.

### Table 2. Results from the Elimination of States Algorithm with fuzzy termination criterion

2000

"... In PAGE 8: ... This last advantage is much more significative when the number of objects increases. On the other hand Table2 shows other results from the experiments after using the above Elimination of States algorithm with a fuzzy termination criterion. It is shown as this algorithm provides a better approximation (lower error) with lower times than Sahni algorithm.... In PAGE 8: ... It is shown as this algorithm provides a better approximation (lower error) with lower times than Sahni algorithm. Results and conclusions pointed out from Table 1 and Table2 are a proof of the... ..."

Cited by 3

### Table 2. Leakage current comparison between heuristics

"... In PAGE 3: ... The state-only assignment was implemented using the approach discussed in [6] while for Vt-only assignment a method similar to the sensitivity based approach dis- cussed in [3] was used. Table2 compares the leakage results obtained with the three pro- posed heuristics for three delay constraints. The columns marked 10%, 25% and 50% refer to leakage minimization where the delay constraints were set at, respectively, 10, 25 and 50% from the all low-Vt circuit delay.... ..."