### Table 1: Examples of number-theoretical true opaque predicates

2002

"... In PAGE 3: ...ssumption 1. Most number-theoretical opaque predicates are complex. By complex, it is meant that the minimal number of arithmetic operations required to resolve them is large, so that the expected resolving time of an adversary is super- polynomial. In particular, the predicates of Table1 are complex. Assumption 2.... In PAGE 4: ...picking random values of DC and then testing if the resulting D4 is prime, or more simply by table lookup. The members of the resulting family of predicates are then treated as the predicates given as examples in Table1 . The value of the variable CP should be determinable at run-time only.... ..."

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### Table 3: Number of theoretical work articles

"... In PAGE 7: ...5 (15%) Other descriptive issues 5 (15%) Total 33 (100%) Table3 shows the number of articles categorised as theoretical works. The majority of them (16 articles, 59%) refers to market modelling issues, followed by 33% (9 articles) denoting to the study of convergence and equilibrium properties.... ..."

### Tables 4 to 6 contain the results obtained when Qd is a number-theoretic rule with quadrature points given by

1997

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### Table 5. Values of D (Qd) using a number-theoretic rule with n = 5003 and j = 1=j

1997

"... In PAGE 8: ...7) with d = 5. In Table5 a large jump in the value of D (Qd) from d = 35 to d = 40 is observed. However, we have no explanation for this behavior.... ..."

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### Table 9. Values of D (Qd) using a number-theoretic rule with d = 20 and j = 1

1997

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### Table 6. Values of D (Qd) using a number-theoretic rule with n = 5003 and j = 1=2j?1

1997

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### Table 10. Values of D (Qd) using a number-theoretic rule with d = 20 and j = 1=2j?1

1997

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### Table 4. Tabulation of Surface Shapes and Total Number of Theoretical Target Surfaces Complementary to Each Molecule in Figure 5

1999

"... In PAGE 10: ... Such a high- resolution adaptation of QSCD brings with it numerical (and thus computational) challenges. 112 negative space cubes (14 8) are now required at the upper limit of theoretical target surface size, translating to exponen- tially greater numbers of theoretical target surfaces and, depending on the stringency of fitting parameters, correspondingly greater numbers of surface fits per molecule as in Table4 . At this resolution, the assump- tion of no occlusions in theoretical target surfaces becomes far less valid, and removal of this assumption increases computational complexity further.... In PAGE 10: ...s a set of 1.1 1014 unique molecular points. Since, using the parameters of this study, an average molecule covers 4.6 million of the unique molecular points bounded by QSCD space ( Table4 ), the model predicts a minimum of (1.1 1014)/(4.... ..."

### Table 1: Mode number, theoretical and experimental frequency and rotational velocity of the tube used for the simulations.

2003

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### Table 1: Examples of number-theoretical true opaque predicates a24 a1a0 a6 a3a2a5a4a7a6

2002

"... In PAGE 3: ...ssumption 1. Most number-theoretical opaque predicates are complex. By complex, it is meant that the minimal number of arithmetic operations required to resolve them is large, so that the expected resolving time of an adversary is super- polynomial. In particular, the predicates of Table1 are complex. Assumption 2.... In PAGE 4: ... This parameter can be generated by picking random values of a0 and then testing if the resulting a66 is prime, or more simply by table lookup. The members of the resulting family of predicates are then treated as the predicates given as examples in Table1 . The value of the variable a96 should be determinable at run-time only.... ..."

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