### Table 1 contains numerical results for the block Jacobi and Gauss Seidel methods applied to the backward Euler equations. The number of iterations required to con- verge to the desired solution increases linearly with the number of timesteps in parallel as predicted by the theory. This negates any potential bene ts from parallelization. 6. Point Jacobi Iterative Schemes. In this section we consider the point Ja- cobi iterative method for the backward Euler method for simplicity. We consider the serial case and analyze the time it takes to solve for a single time step. 6.1. Backward Euler. For the conventional backward Euler scheme the itera- tion matrix is given by

### Table 2: Properties of derived graphs. G0 belongs to G belongs to Production applied FULLTREEdecide(n; 2n; 0) TREEdouble(n + 1; 2n; 0)

1996

Cited by 69

### Table 2: Properties of derived graphs. G0 belongs to G belongs to Production applied FULLTREEdecide(n; 2n; 0) TREEdouble(n + 1; 2n; 0)

1996

Cited by 69

### Table 1. A compositional table for C4

"... In PAGE 9: ... In this group there are eight rotations: e, R90, R902, R903, H, V, R90H, R90V. Under Table1 we investigated the group of symmetries of a Ruby cell. We look for cyclic subgroups of the group C4.... ..."

### Table 1. Simulation results for sort routine execution (nodes 1-5).

### Table 1: The number of transitions in some case studies. The rst two examples in Table 1 were two speci cations for an early data link layer commu- nication protocol, which was in [16] shown to behave incorrectly. The speci cation lts apos;s had 11 and 12 global states, respectively. With the help of the CWB, we found observation equivalent lts apos;s with the minimal number of states { 3 and 4 states. However, the number of transitions (14 and 19) could still be reduced (to 4 and 5). In Figure 5 two lts apos;s with the minimal number of states are shown in the case of the latter speci cation; the lts i) was returned by the CWB whereas ii) has the minimal number of transitions.

"... In PAGE 11: ... However, it does not minimize the number of transitions, but returns a saturated ts without -loops. In some case studies [8] our minimization algorithm given in Figure 3 reduced the number of transitions considerably ( Table1 ). From the minimized ts it is easier to study the relevant features of the system.... In PAGE 12: ...Table1 was a physical layer protocol, namely an asynchronous start-stop protocol described in [10]. The speci cation lts had 103 global states.... In PAGE 12: ... The CWB gave us 17 transitions, while the minimal number of transitions was 10. The last example in Table1 was an application layer protocol describing the behaviour of an association control service element [1] [2]. The speci cation lts had 40 global states, and it could be reduced to an lts with 21 states.... In PAGE 12: ... Especially, we showed that the number of transitions can be minimized, and that the minimal ts is unique. The result is useful in practice, since it may reduce the minimal ts considerably ( Table1 ). Moreover, it is interesting to notice that the minimal amount of information about a ts can be selected only in one way; it could be the case that two di erent subsets of transitions in a saturated ts would contain the same information.... ..."

### Table 8. Combination of Operators

"... In PAGE 11: ... Transformation rules inspired from Lee et al. [8] and detailed in Table8... ..."