### Table 1: Hardness versus randomness trade-o s for AM. If the hardness condition on the left-hand side of Table 1 holds for in nitely many input lengths, then the corresponding derandomization on the right-hand side works for in nitely many input lengths. Similar weak interpretations hold for all our results. As a corollary to the weak version of Table 1, we obtain that every language in AM, and graph nonisomorphism in particular, has subexponential size proofs for in nitely many input sizes unless the polynomial-time hierarchy collapses.Using other hardness measures and various oracles B, we get derandomization results for other complexity classes. We summarize the situation in Table 2. lower bound on: derandomizes:

1998

"... In PAGE 2: ... We show that the existence of an exponential-time decidable language with high worst-case nonuniform complexity when the circuits have access to an oracle for satis ability, implies nontrivial derandomizations of AM-games. The trade-o s are presented in Table1 . We use CB to denote circuit complexity given access to oracle B, and similarly ~ CB given only parallel access to the oracle.... In PAGE 2: ... See Section 2 for precise de nitions. The parameter s in Table1 can be any space constructible function, the interesting range lying between logarithmic and subpolynomial, e.... In PAGE 8: ...4 and 3.13 to the nondeterministic setting, and thus relax the hardness assumptions in Table1 from circuit complexity for parallel access to SAT to nondeterministic circuit complexity .... ..."

Cited by 2

### Table 3: Hardness versus randomness trade-o s for MA. Theorem 4.2 If NEXP \ coNEXP 6 P=poly, then MA \ gt;0i.o.-NTIME[2n ]. Consequently, if MA does not have subexponential size proofs for in nitely many lengths, then NEXP \ coNEXP P=poly, which implies that EXP = p 2 \ p 2, hence that the polynomial-time hierarchy collapses to the second level. Finally, by looking at oracle circuits instead of parallel oracle circuits, we can derandomize BPPB for any oracle B, given an exponential-time computable predicate with high circuit complexity relative to B. Replacing ~ C by C, ~ H by H, and dropping the parallel in Theorems 3.2 and 3.11 and their proofs, yields the derandomization results of Table 4. Both A and B represent arbitrary oracles.

1998

Cited by 2

### Table 1: Wilkinson polynomial timings

1998

"... In PAGE 20: ... 7.1 Univariate Root Finding Table1 presents some timing results for univariate root nding. The exam- ples are from the family of Wilkinson polynomials W n (x)= Y i=1... ..."

Cited by 2

### Table 2. Speedup in Worst-Case Execution Time for Optimized Virtual Table Algorithm

"... In PAGE 5: ... However, for the OVTA, the optimiza- tion over VTA depends completely on the characteristics of the generator polynomial chosen. Table2 shows the improvement over the VTA for several different polyno- mials (refer to Section 4 for a description of CRC32sub8 and CRC32sub16) . Note that for the particular CRC24 and CRC32 polynomials we used for our experiments, the OVTA has no improvement at all over the VTA.... ..."

### Table 1. Memory Hierarchy

"... In PAGE 11: ... The simulator models a 6-issue processor with 2 memory read ports, 2 memory write ports, 4 integer units, 1 floating point unit, and 1 branch unit. The config- uration of the memory hierarchy is given in Table1 . The memory behavior of StarDBT itself is not simulated since the execution time spent in StarDBT code is a small fraction of the execution time of the entire program.... ..."

### Table 1. Memory Hierarchy

"... In PAGE 11: ... The simulator models a 6-issue processor with 2 memory read ports, 2 memory write ports, 4 integer units, 1 floating point unit, and 1 branch unit. The config- uration of the memory hierarchy is given in Table1 . The memory behavior of StarDBT itself is not simulated since the execution time spent in StarDBT code is a small fraction of the execution time of the entire program.... ..."

### Table 1: Succinctness of target compilation languages. A3 means that the result holds unless the polynomial hierarchy collapses.

2001

"... In PAGE 4: ... Proposition 3.1 The results in Table1 hold. Figure 5 summarizes the results of Proposition 3.... In PAGE 4: ...1, which explains why some of its parts are conditioned on the polyno- mial hierarchy not collapsing. We have excluded the subsets BDD, s-NNF, d-NNF and f-NNF from Table1 since they do not qualify as target com- pilation languages (see Section 4). We kept NNF and CNF though given their importance.... In PAGE 4: ... We kept NNF and CNF though given their importance. Consider Figure 5 which de- picts Table1 graphically. With the exception of NNF and CNF, all other languages depicted in Figure 5 qualify as target compilation languages.... ..."

Cited by 21

### Table 6: Design time of the hierarchy reducing

2002

"... In PAGE 4: ...able 5: Results for JPEG and Vocode Project Examples .................................................................................... 10 Table6... In PAGE 17: ... Manual Hierarchy Reducing We randomly generate 3 examples, each of which contains no more than 10 behaviors. Table6 shows design time of the manual hierarchy reducing and automatic reducing using spec optimizer. Table 6: Design time of the hierarchy reducing... ..."

Cited by 2

### Table 1: Calculation time of hierarchy in seconds.

2001

"... In PAGE 6: ... The datasets were segmented as presented in Section 3. Table1 shows the time for the calculation of the hierarchical octrees for the tibia fracture, the cow foot and the hand bones. Table 1: Calculation time of hierarchy in seconds.... ..."

Cited by 1

### Table 6. Complexity data of hierarchies

"... In PAGE 14: ... Because the computation time for a coloring is small compared to the time needed to construct the con ict graph, it makes sense to try all four algorithms and take the best result. Table6 gives more data on the characteristics of the di erent type hierarchies with respect to the algorithm. It is evident that in most hierarchies the number of types which need their own gene is small compared to the number of types with multiple super types.... ..."