# Transforming Group Codes in Mealy Finite State Machines with Composite State Codes
## 6 Experimental Results
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Benchmark** & **L** & **N** & **H** & **M** & **L + R** \\ \hline bbara & 4 & 2 & 60 & 10 & 8 \\ bbse & 7 & 7 & 56 & 16 & 11 \\ bbtas & 2 & 2 & 24 & 6 & 5 \\ beecount & 3 & 4 & 28 & 7 & 6 \\ cse & 7 & 7 & 91 & 16 & 11 \\ dk14 & 3 & 5 & 56 & 7 & 6 \\ dk15 & 3 & 5 & 32 & 4 & 5 \\ dk16 & 2 & 3 & 108 & 27 & 7 \\ dk17 & 2 & 3 & 32 & 8 & 5 \\ dk27 & 1 & 2 & 14 & 7 & 4 \\ dk512 & 1 & 3 & 15 & 15 & 5 \\ donfile & 2 & 1 & 96 & 24 & 7 \\ ex1 & 9 & 19 & 138 & 20 & 14 \\ ex2 & 2 & 2 & 72 & 19 & 7 \\ ex3 & 2 & 2 & 36 & 10 & 6 \\ ex4 & 6 & 9 & 21 & 14 & 10 \\ ex5 & 2 & 2 & 32 & 9 & 6 \\ ex6 & 5 & 8 & 34 & 8 & 8 \\ ex7 & 2 & 2 & 36 & 10 & 6 \\ keyb & 7 & 7 & 170 & 19 & 12 \\ kirkman & 12 & 6 & 370 & 16 & 16 \\ lion & 2 & 1 & 11 & 4 & 4 \\ lion9 & 2 & 1 & 25 & 9 & 6 \\ mark1 & 5 & 16 & 22 & 15 & 9 \\ mc & 3 & 5 & 10 & 4 & 5 \\ modulo12 & 1 & 1 & 24 & 12 & 5 \\ opus & 5 & 6 & 22 & 10 & 9 \\ planet & 7 & 19 & 115 & 48 & 13 \\ planet1 & 7 & 19 & 115 & 48 & 13 \\ Pma & 8 & 8 & 73 & 24 & 13 \\ s1 & 8 & 7 & 106 & 20 & 13 \\ s1488 & 8 & 19 & 251 & 48 & 14 \\ s1494 & 8 & 19 & 250 & 48 & 14 \\ s1a & 8 & 6 & 107 & 20 & 13 \\ s27 & 4 & 1 & 34 & 6 & 7 \\ s298 & 3 & 6 & 1096 & 218 & 11 \\ \hline \end{tabular}
\end{table} 
Table 7: Characteristics of benchmarks from LGSynth93 [38]. Tables 8-11 include the following columns: FSM (names of benchmark FSMs); MB (experimental results for MBC-based FSMs); OH (experimental results for OHC-based FSMs); JEDI (experimental results for FSMs with state codes generated by JEDI); \(U_{2}\) (experimental results for FSMs with composite state codes); and \(U_{3}\) (experimental results obtained for our new approach). The results of the summation of values from the corresponding columns are shown in the row \"Total\". The row \"Percentage\" shows the percentage of the summarized characteristics of the investigated FSM circuits compared to those of \(U_{3}\)-based FSMs. The main goal of the proposed method was increasing the performance of LUT-based FSM circuits in relation to the circuits of FSMs based on composite state codes. So, the most important characteristic was the cycle time (or operating frequency). The values for the cycle times were obtained directly from Vivado reports. These values are shown in Table 8.  
As follows from Table 8, the proposed method made it possible to obtain LUT-based FSM circuits with shorter cycle times than those of the other studied FSMs. As can be seen \begin{table}
\begin{tabular}{c c c c c c} \hline
**Benchmark** & **L** & **N** & **H** & **M** & **L + R** \\ \hline s386 & 7 & 7 & 64 & 13 & 11 \\ s510 & 19 & 7 & 77 & 47 & 25 \\ s8 & 4 & 1 & 20 & 5 & 7 \\ s820 & 18 & 19 & 232 & 25 & 23 \\ s832 & 18 & 19 & 245 & 25 & 23 \\ sand & 11 & 9 & 184 & 32 & 16 \\ shiftreg & 1 & 1 & 16 & 8 & 4 \\ sse & 7 & 7 & 56 & 16 & 11 \\ styr & 9 & 10 & 166 & 30 & 14 \\ tma & 8 & 9 & 44 & 20 & 13 \\ \hline \end{tabular}
\end{table} 
Table 7: _Cont._  
\begin{table}
\begin{tabular}{l c c c c c c} \hline
**FSM** & **MB** & **OH** & **JEDI** & \(\mathbf{U_{2}}\) & \(\mathbf{U_{3}}\) & **L + R** \\ \hline ex1 & 6625 & 7155 & 5654 & 3620 & 3410 & 16 \\ \hline kirkman & 7073 & 6494 & 6382 & 4359 & 3993 & 18 \\ \hline planet & 7535 & 7535 & 5344 & 3491 & 3321 & 14 \\ planet1 & 7535 & 7535 & 5344 & 3491 & 3321 & 14 \\ pma & 6841 & 6841 & 5888 & 4080 & 3708  
from Table 8, \(U_{3}\)-based FSMs had the following improvements in cycle times: (1) 82.25% compared with MBC- based FSMs; (2) 84.37% compared with OHC-based FSMs; (3) 60.28% compared with JEDI-based FSMs; and (4) 8.81% compared with \(U_{2}\)-based FSMs. An analysis of Table 8 shows that under some conditions, our method always produced circuits that were slightly faster than the circuits of the equivalent FSMs with composite state codes, but the level of improvement depended on the value of \(L+R\). For example, we found \(L+R=13\) for the benchmark \(tma\). As follows from Table 8, our method provided an improvement of around 1%. Next, we found \(L+R=27\) for the benchmark s510.