### Table 1: Stochastic testing scheme.

"... In PAGE 3: ... In this quot;on-line quot; model, the program is tested as it is be ing trained, and the learning is terminated as soon as it succeeds on enough number of consecutive random ex amples. The testing scheme, described in Table1 , has a slightly better bound on the number of test examples than that of [Angluin, 1988]. Definition 2 A problem solver f for a domain D and a problem distribution P satisfies a sparse solution space bias if there is a set of operator sequences mf such that, on any problem and is bounded by a polynomial Q in the problem size n.... ..."

### Table 4: Average number of iterations (out of 1000) that converged to the joint action for the partially stochastic game.

in Abstract

"... In PAGE 5: ... This im- provement in performance was partly due to the fact that the Penalty game has twice the number of optimal solu- tions to which learning may converge. The results for the partially stochastic Climbing game ( Table4 ) were similar (although more extreme) to the ones in the deterministic Climbing game from Table 2. FMQ and LMRL were again the smarter algorithms: they found the optimal joint action in almost all runs when paired with themselves or each other.... ..."

### Table 1: Area/throughput design results of stochastic ray tracing formfactor calculations on Xilinx Virtex family FPGAs.

"... In PAGE 2: ... Appropriate throughput/area arithmetic cores are then automatically instantiated for arithmetic op- erations from a device-independent arithmetic library written in Handel-C, or a database of device-specific cores pregenerated using Xilinx Coregen. Table1 demonstrates how the design pattern is used to automatically scale performance for different size FPGAs in the Xilinx Virtex series. For each de- vice, the entire throughput/area design space is de- termined by exhaustive compilation.... ..."

### Table 10: Parameters for Stochastic Experiments

"... In PAGE 32: ... In these experiments, we do not consider LAMA because its control structure is not suited to stochastic problems. The data parameters in Table10 are used to construct the stochastic experiment data sets and are similar to the #0Crst set of deterministic experiments. The main exception is the single period time windows on the tasks that enables an optimal posterior bound to be calculated.... ..."

### Table 3: Stochastic problem data.

"... In PAGE 5: ...re independent of each other. This in reality, however, is rarely the case. These unit quantities, or coefficients, can and will exhibit variation, and the assumptions have some degree of relationship to each other. Consider Table3 , showing the modification of these coefficients reflecting the more realistic stochastic behavior, and Table 4, showing correlations between the assumptions. Determining a feasible combination of x1 and x2 so as to optimize the profit now becomes more difficult given that the coefficients exhibit variability, along with their interrelationships.... ..."

### Table 5: Optimal values for scenarios and stochastic solution in high supply case

"... In PAGE 9: ...2 Expected 6,560,653 5,967,769 592,884 90.9 Table 6: Worst case analysis for high supply case Table5 shows the di erences between the revenue given by the optimal solution of each scenario and the revenue given by the stochastic solution for the same scenario. The expected revenue generated by the... ..."

### Table 4: Correlations between assumptions for stochastic optimization problem.

"... In PAGE 5: ...re independent of each other. This in reality, however, is rarely the case. These unit quantities, or coefficients, can and will exhibit variation, and the assumptions have some degree of relationship to each other. Consider Table 3, showing the modification of these coefficients reflecting the more realistic stochastic behavior, and Table4 , showing correlations between the assumptions. Determining a feasible combination of x1 and x2 so as to optimize the profit now becomes more difficult given that the coefficients exhibit variability, along with their interrelationships.... ..."