# Improving Symbolic System-Level Synthesis by Solver Coordination and Domain-Specific Heuristics
## 8 Experimental Results
### Experimental Results
#### 8.3.2 Results of Coordinated Approach
Regarding the number of couplings between logic solver and background theory, this number varies on average between 3 and 6. Note that the number of required couplings to find a feasible synthesis in all experiments of the work at hand is generally reduced. Here, the addition of the Korst-constraint (cf. Equation (2)) in the answer set solver, missing in previous approaches [26; 27], already ensures that all pairwise computational task combinations on a tile are schedulable and potential pairwise scheduling conflicts are not encountered in the background theory anymore. The changed distribution of efforts in Figure 7 between answer set solving and background theory solver compared to the _classical_ approach becomes more prominent if one computes the quotient of averaged runtimes of the time spent in the background theory divided by the time spent in the answer set solver. This quotient is between 70 and 600 for all instances with 3 \(\times\) 3 mesh grids in the _classical_ approach, whereas the quotient is in the range 2-10 for all instances with any investigated mesh grid size in the _coordinated_ synthesis approach. Thus, w.r.t. to the share of the overall solving time in the _coordinated_ approach, considerable more effort is shifted to the answer set solver. However, as already indicated earlier, starting with the 5 \(\times\) 5-70 instances, also the _coordinated_ approach reaches its limits. The Tables 3-5 capture three different categories of timeout runs of the _coordinated_ approach. Here, the runs reaching the set timeout for a synthesis run can be divided into two categories: Table 3 shows selected data of runs of different instance sets where a synthesis run is dominated by the average time the coordinated approach spends within the background  
Figure 7: Overview of the average distribution of runtimes of the successful runs using the _coordinated_ approach and the _coordinated_+_DSH_ approach for all instance sets. The vertical error bars show the standard deviation. theory. This is similar to what we saw in the results for the _classical_ approach but now we make this observation at considerable harder instance sets. However, as a new observation, Table 4 shows average times of synthesis runs where the runtime until the timeout is mainly dominated by the answer set solver. In these cases, the answer set solver could not find a new binding and routing candidate in the meanwhile restricted search space after a few couplings with the background theory solver. The final and third category is that for larger instances the background theory allocates memory reaching the overall synthesis memory limit and thus the synthesis run is canceled (cf. Table 5). Thereby, the memory limit is always reached in the last stage of the hierarchical scheduling scheme where the schedulability of independent app clusters is decided. However, in these cases there is always only one large application cluster resulting in scheduling problems spanning all hardware resources (PEs, NIs and routers) of the hardware platform. As a consequence, these scheduling problems are too memory intense to decide given our memory limit of 62 GB RAM. All the results presented in Tables 3-5 are not desired as they limit the scalability of the _coordinated_ synthesis approach, especially in the 6 \(\times\) 6 mesh grid regime at higher utilization (cf. Table 2). Thus, we enhanced the _coordinated_ synthesis approach by including domain-specific heuristics within the answer set solver. Again, the goal was to have \"nicer\" solutions proposed to the background theory which can be decided within reasonable time and without running into memory limitations. Furthermore, another goal was to reduce the occurring long solving times in the answer set solver as observed for some 6 \(\times\) 6 mesh grid instances (cf. Table 4).