### Table 3: Total Execution time (in seconds) for our parallel state assignment algorithm on a Sun E4500 multiprocessor.

2004

"... In PAGE 12: ... Figure 3 shows the total execution time for different FSMs on multiprocessor runs. ( Table3 in the appendix provides detailed running times.) The reported speedups are good for all problem sizes (number of states) but are higher for larger problem sizes.... ..."

### Table 1. Execution time, number of visited states and improvement wrt initial state

"... In PAGE 8: ... 4.3 Experimental results In order to validate our method, we implemented the proposed algorithms in C++ and experimented on the variation of measures like time (we present it in Table1 as the volume of visited states), volume of processed rows, improvement and quality of the proposed workflow. We have used a simple cost model taking into consideration only the number of processed rows based on simple formulae [17] and assigned selectivities for the involved activities.... In PAGE 9: ...consequently, for medium and large cases we compare (quality of solution) the best solution of HS and HS-Greedy to the best solution that ES has produced when it stopped (Table 2 and Figure 9). Table1 depicts the number of visited states for each algorithm, and the percentage of improvement for each algorithm compared with the cost of the initial state. We note that for small workflows, HS provides the optimal solution according to ES.... ..."

### Table 1. Execution time, number of visited states and improvement wrt initial state

"... In PAGE 8: ... 4.3 Experimental results In order to validate our method, we implemented the proposed algorithms in C++ and experimented on the variation of measures like time (we present it in Table1 as the volume of visited states), volume of processed rows, improvement and quality of the proposed workflow. We have used a simple cost model taking into consideration only the number of processed rows based on simple formulae [17] and assigned selectivities for the involved activities.... In PAGE 9: ...consequently, for medium and large cases we compare (quality of solution) the best solution of HS and HS-Greedy to the best solution that ES has produced when it stopped (Table 2 and Figure 9). Table1 depicts the number of visited states for each algorithm, and the percentage of improvement for each algorithm compared with the cost of the initial state. We note that for small workflows, HS provides the optimal solution according to ES.... ..."

### Table 3: Running times in seconds for the parallel algorithm

1996

"... In PAGE 8: ... The state storage-based parallel algorithm in Figure 5 is based on the definitions of these partitions. Experimental results are presented in Table3 to demon- strate the improvements in runtimes for the state storage- based parallel algorithm. Results are presented in terms of runtimes in seconds with the number of processors varying from 1 to 8.... ..."

Cited by 1

### Table 3: Parallel Shortest Path Algorithm

1997

"... In PAGE 4: ... Our parallel shortest path algorithm uses the SPMD model for which each processor solves the portion of the shortest path tree on its subnetwork for each source. The outline of the algorithm is given in Table3 . Each processor repeatedly solves for shortest paths for its assigned subnetwork.... ..."

Cited by 7

### Table 3: Parallel Shortest Path Algorithm

1997

"... In PAGE 4: ... Our parallel shortest path algorithm uses the SPMD model for which each processor solves the portion of the shortest path tree on its subnetwork for each source. The outline of the algorithm is given in Table3 . Each processor repeatedly solves for shortest paths for its assigned subnetwork.... ..."

Cited by 7

### Table 2: Number of product terms for PSTISIG state assignment.

1993

"... In PAGE 5: ...ig. 9: Synthesis process for controllers with MISR state registers. 4 Results The algorithm was programmed in C and evaluated with the examples from the MCNC benchmark set WCNC 881. The resulting numbers of product terms for the largest bench- marks are summarized in Table2 . The branch-and-bound algorithm was parameterized such that the run time for state assignment was in the range of minutes on a SUN 4/60.... ..."

Cited by 2

### Table 2. State assignment

"... In PAGE 2: ... These code words are assigned such that transitions from the newly assigned states to those already assigned or vice-versa, require change in the minimum number of state bits; however, this may not always be possible. Column 2 of Table2 shows a possible code word assignment for states for B, C, and D. Note that this assignment ensures minimum transitions from A to B, A to C, C to D and C to F, but four bits change during transition from B to D.... In PAGE 2: ... The refinement process i n - volves selective changing and/or exchanging assigned code words to the states. Column 3 of Table2 shows the refined state assignment obtained by changing the code words for states A, B and C in column 2 to 01010, 10010 and 01100 respe c -... ..."

### Table 3: state assignment

"... In PAGE 5: ...Thestatetable for the BCD detector after state reduction is shown in Table 2. Table 2: state of detector Next state Output R Present state 0 = T 1 = T 0 = T 1 = T ABB00 BCD00 CEF00 DFF00 EAA00 FAA01 A conventional state assignment using state variables ) , , ( z y x is shown by the conventional encoding column in Table3 . Since the states are all uni-coded, there are two redundant states.... ..."