# Area and Performance Estimates of Finite State Machines in Reconfigurable Systems
## 2 Related Works
### Estimates of FSMs
#### 3.2.3 Other Estimates for FSMs
Figure 3 shows the graphs of the efficiency of the considered estimates in terms of area. Here, the estimates are assigned place numbers by the average area value (_Average_) according to the order given above, with the _avg_dec_ estimate having the highest number 7 and the _diff_w_ estimate having the lowest number 1. According to Figure 3, the ranking in terms of average area value (_Average_) approximately corresponds to the number of best solutions (_Best_). ### Results with Respect to the FSM Performance

The results of the studies with respect to performance are summarized in Tables 8 and 9, where \(F1\),\(\ldots\),\(F7\) are the maximum frequency of the FSM operation (in megahertz) using the corresponding estimate; \(Fmax\) is the maximum frequency value for a particular example; \(Fmax/F1\),\(\ldots\), \(Fmax/F7\) are the ratios of the corresponding parameters; and _Best_, _Unique_, and _Av_ meaning as before. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**FSM**} & \multirow{2}{*}{ \begin{tabular}{c} _e_FPGA_ \\ _LI1/Lmin_ \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} _classic_ \\ _L2/Lmin_ \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} _diff_w_ \\ _L3/Lmin_ \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} _max_w_ \\ _L4/Lmin_ \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} _seq_dec_ \\ _L4/Lmin_ \\ \end{tabular}  } & \multirow{2}{*}{\ \begin{tabular}{c} _par_dec_ \\ _L5/Lmin_ \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} _avg_dec_ \\ _L6/Lmin_ \\ \end{tabular}  } \\ \hline bbara & 1.231 & 1.000 & 1.423 & 1.077 & 1.231 & 1.231 & 1.231 \\ bbsse & 1.130 & 1.130 & 1.204 & 1.000 & 1.056 & 1.222 & 1.056 \\ beecount & 1.000 & 1.056 & 1.111 & 1.056



Figure 3: Efficiency by area of the estimates considered: _Average_ is the place in order by average value area; _Best_ is the number of best solutions; _Unique_ is the number of unique solutions. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{**FSM**} & \multirow{2}{*}{ \begin{tabular}{c} _e_FPGA_ \\ _F_**1** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} _classic_ \\ _F_**2** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} _diff\_w_ \\ _F_**3** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} _max\_w_ \\ _F_**4** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} _seq\_dec_ \\ _F_**5** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} _par\_dec_ \\ _F_**6** \\ \end{tabular}  } & \multirow{2}{*}{\ \begin{tabular}{c} _avg\_dec_ \\ _F_**7** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} _Fmax_ \\ _F_**8** \\ \end{tabular}  } \\ \hline bbara & 430 & **529** & 414 & 453 & 430 & 430



Table 9 shows that with respect to the best performance solution on average (parameter _Av_), the estimates can be arranged in the following order:

_classic_--1.055;

_avg_dec_--1.069;

_par_dec_--1.071;

_max_w_--1.072;

_seq_dec_--1.080;

_e_FPGA_--1.088;

_diff_w_--1.113. Unexpectedly, the best in terms of performance on average is the _classic_ estimate, which is designed to determine the FSM area. The _classic_ estimate also achieves the highest number of best (11) and unique (10) solutions (Table 8). The _classic_ estimate is expectedly followed by the _avg_dec_ and _par_dec_ estimates, which on average perform reasonably well in terms of performance. This is followed by the _max_w_, _seq_dec_, and _e_FPGA_ estimates. The _diff_w_ estimate shows noticeably worse results (1.113). However, the _diff_w_ estimate reaches the 5 best solutions, among which 4 solutions are unique. Given the reported results, we recommend that to find the best solution in terms of performance, all estimates should be applied because each estimate can achieve the best