### Table 3: Reachability analysis of the game Four Connect (cont.)

2002

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### Table 3: Reachability analysis of the game Four Connect (cont.)

"... In PAGE 78: ...3 466.8 Table3 : Upper bound results for SetA* on the D9V 4M15 problem. u is the upper bound, #it is the number of itera- tions, T is the total CPU time, Tt is the time used to generate the improvement partitioning, and Ts is time used on search.... In PAGE 78: ... in the search queue. The results are shown in Table3 and were obtained for the D9V 4M15 problem using the same disjunctive partitioning as in the previous experiment. As depicted the performance degrades substantially for large values of u.... ..."

### Table 3: Reachability analysis of the game Four Con- nect (cont.)

### Table 3: Reachability analysis of the game Four Connect (cont.)

"... In PAGE 76: ...3 466.8 Table3 : Upper bound results for SetA* on the D9V 4M15 problem. u is the upper bound, #it is the number of itera- tions, T is the total CPU time, Tt is the time used to generate the improvement partitioning, and Ts is time used on search.... In PAGE 76: ... in the search queue. The results are shown in Table3 and were obtained for the D9V 4M15 problem using the same disjunctive partitioning as in the previous experiment. As depicted the performance degrades substantially for large values of u.... ..."

### Table 1. Comparison of sequential and concurrent probabilistic processes

"... In PAGE 9: ... (13), it makes sense for a Markov net (N, P) and for a reachable marking m, to use the notations: Pm, Em, (14) to respectively denote the probability Pv and the expectation Ev for any finite configuration v with positive likelihood, and such that m = m(v), provided that such a v exists. Table1 summarizes and compares the definitions introduced so far, and em- phasizes the symmetry between sequential and concurrent systems. Table 1.... ..."

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### Table 2: Reachability analysis of the game Four Connect. The numbers of BDD nodes and represented reached and new states for each step l in the exploration are depicted.

"... In PAGE 15: ...71% LA39 15 15 1233 1221 1221 1283 4.83% Table2 : The results of our implementation on the bench- marks. Columns #j and #m indicated the number of jobs and machines, followed by the best known results for non- preemptive scheduling, the known optimum for the preemp- tive case, the results of Le Pape and Baptiste, followed by our results and their deviation from the optimum.... In PAGE 54: ... The convergence proofs for the original LAO* algorithm carry over in a straightforward way to symbolic LAO*. Experimental results Table2 compares the performance of symbolic LAO* and SPUDD on the factory examples (f to f6) used by Hoey et al.(1999) to test the performance of SPUDD, as well as addi- tional test examples (r1 to r4) that correspond to randomly- generated MDPs.... In PAGE 55: ...2 7.4 gt; 20hr Table2 : Performance comparison of LAO* and SPUDD. time of value iteration.... In PAGE 55: ... Use of an admissible heuristic to limit the search space is charac- teristic of heuristic search, in contrast to simple reachability analysis. As Table2 shows, LAO* evaluates much less of the state space than simple reachability analysis. The better the heuristic, the smaller the number of states it examines.... In PAGE 63: ...rial, is .0046 and .000019, respectively. Table 1 indicates a speed-up of two orders of magnitude on the larger scenarios, numbers 9-11, using DAP. Table2 shows the state space reductions achieved by ex- ploiting the implicit representation. This table compares the total number of states visited by each verifier in the course of controller synthesis.... In PAGE 64: ...Forward RTA Forward CSV DAP RTA DAP CSV 1 30 30 30 33 2 34 34 33 33 3 15 15 15 15 4 18 18 18 18 5 153147 229831 170325 3069 6 122 120 500 54 7 2826 5375 631 83 8 146 131 301165 24065 9 4361 4799 163133 259 10 219885 129329 184972 871 11 219885 129329 189184 871 12 585 513 509 99 13 685 675 1782 93 14 106 106 141 142 15 17 17 1054 1389 16 117 101 131 116 17 27 27 29 25 18 284 290 355 269 19 18 18 18 18 20 63 60 33 34 Table2 : Comparison of state spaces explored with different search strategies (Forward and DAP), timed automaton verifier (RTA) versus CIRCA-specific verifier (CSV).... In PAGE 79: ...2 - TIME - TIME 11 34 39.3 - TIME - TIME - TIME 12 - MEM - TIME - TIME - TIME Table2 : Results for the DxV 4M15 problem. #it is the number of iterations, and T is the total CPU time.... ..."

### Table 2: Reachability analysis of the game Four Connect. The numbers of BDD nodes and represented reached and new states for each step l in the exploration are depicted.

"... In PAGE 13: ...71% LA39 15 15 1233 1221 1221 1283 4.83% Table2 : The results of our implementation on the bench- marks. Columns #j and #m indicated the number of jobs and machines, followed by the best known results for non- preemptive scheduling, the known optimum for the preemp- tive case, the results of Le Pape and Baptiste, followed by our results and their deviation from the optimum.... In PAGE 52: ... The convergence proofs for the original LAO* algorithm carry over in a straightforward way to symbolic LAO*. Experimental results Table2 compares the performance of symbolic LAO* and SPUDD on the factory examples (f to f6) used by Hoey et al.(1999) to test the performance of SPUDD, as well as addi- tional test examples (r1 to r4) that correspond to randomly- generated MDPs.... In PAGE 53: ...2 7.4 gt; 20hr Table2 : Performance comparison of LAO* and SPUDD. time of value iteration.... In PAGE 53: ... Use of an admissible heuristic to limit the search space is charac- teristic of heuristic search, in contrast to simple reachability analysis. As Table2 shows, LAO* evaluates much less of the state space than simple reachability analysis. The better the heuristic, the smaller the number of states it examines.... In PAGE 61: ...rial, is .0046 and .000019, respectively. Table 1 indicates a speed-up of two orders of magnitude on the larger scenarios, numbers 9-11, using DAP. Table2 shows the state space reductions achieved by ex- ploiting the implicit representation. This table compares the total number of states visited by each verifier in the course of controller synthesis.... In PAGE 62: ...Forward RTA Forward CSV DAP RTA DAP CSV 1 30 30 30 33 2 34 34 33 33 3 15 15 15 15 4 18 18 18 18 5 153147 229831 170325 3069 6 122 120 500 54 7 2826 5375 631 83 8 146 131 301165 24065 9 4361 4799 163133 259 10 219885 129329 184972 871 11 219885 129329 189184 871 12 585 513 509 99 13 685 675 1782 93 14 106 106 141 142 15 17 17 1054 1389 16 117 101 131 116 17 27 27 29 25 18 284 290 355 269 19 18 18 18 18 20 63 60 33 34 Table2 : Comparison of state spaces explored with different search strategies (Forward and DAP), timed automaton verifier (RTA) versus CIRCA-specific verifier (CSV).... In PAGE 77: ...2 - TIME - TIME 11 34 39.3 - TIME - TIME - TIME 12 - MEM - TIME - TIME - TIME Table2 : Results for the DxV 4M15 problem. #it is the number of iterations, and T is the total CPU time.... ..."

### Table 2: Reachability analysis of the game Four Connect. The numbers of BDD nodes and represented reached and new states for each step l in the exploration are depicted.

2002

Cited by 3

### Table 3 Linear relationship between the integrated results and the number of concurrent players

in M. Ye

"... In PAGE 9: ... On the other hand, if every server followed Equation 10, the number of concurrent players for the entire game world would follow Equation 13. Table3 shows the results for the entire game world. Cov(k0, k) indicates that the linear relationship is improved (see the brown line in Figure 4).... ..."

### Table 1 Attributes of 3 Gaming Paradigms

2006

"... In PAGE 5: ...5 systems. MMORPGs are a new paradigm in computer gaming (see Table1 ). By definition, MMORPG users are part of a persistent world of up to 2000 other concurrent users (Sony Online, 2003).... ..."

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