## 7 Generalized FSM Architecture
We hope that all the presented steps of this method are clear from the previous text. We do not, however, consider this method in detail. This will be the subject of a separate study. Now we will show that the generalized architecture (Figure 13) generates 6 more architectures. Three conditions are used for this purpose. The fulfillment of condition (18) indicates the presence of the block _CoreFC_ in the FSM circuit architecture. This means that the set \(S^{0}\) contains at least one element. The fulfillment of condition (35) indicates the presence of the block _CoreFD_. In this case, the set \(S3\) contains at least one element. Finally, the fulfillment of the condition  
Figure 12:1  
indicates the presence of the block _CorePC_. In this case, the set \(S2\) contains at least one element. We show the possible FSM models in Figure 12:2 Additionally, the table rows contain conditions (or their conjunctions) in which a particular architecture should be used. The first three columns of the table contain the names of the sets (\(S^{0}\), \(S2\), \(S3\)) and corresponding architectural blocks (_CoreFC_, _CorePC_, _CoreFD_). The fourth column contains the model designation. The fifth column shows which combination of conditions leads to the model from a particular row. If there is a zero (one) at the intersection of the column \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(S^{0}\) & \(S2\) & \(S3\) & **Model** & **Conditions** \\ \hline
**FC** & **PC** & **FD** & & \\ \hline
0 & 0 & 1 & \(P_{F}Y\) & (35) \\
0 & 1 & 0 & \(P_{T}Y\) & (42) \\
0 & 1 & 1 & \(P_{FT}Y\) & (35) and (42) \\
1 & 0 & 0 & \(PY\) & (18) \\
1 & 0 & 1 & \(P_{FF}Y\) & (18) and (35) \\
1 & 1 & 0 & \(P_{2T}Y\) & (18) and (42) \\
1 & 1 & 1 & \(P_{F2T}Y\) & (18), (35), and (42) \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Possible FSM models. with the block and the row with the model, then this block is not included (is included) in the FSM architecture corresponding to this row. For example, if all states satisfy condition (35), then the architecture includes only _CoreFD_. We denote this architecture by the symbol \(P_{F}Y\). This is the first row of Table 11. If some of states satisfy condition (35) and others satisfy condition (42), then the architecture includes blocks _CorePC_ and _CoreFD_ (row 3). This leads to \(P_{FT}Y\) FSMs, and so on. The last row corresponds to the generalized FSM architecture, including three cores of partial functions. Using Table 11 and generalized architecture, we can obtain the architecture for any model represented by this table. Obviously, it is possible to transform the design method for \(P_{F2T}Y\) FSMs into a design method for any other model. In this case, of particular interest is the implementation of Step 2 of the proposed method and the definition of a model corresponding to its outcome. We have presented the algorithm for performing these steps in Figure 14.  
Let us consider this algorithm. Block 1 shows the initial information (FSM is represented by STG and the FPGA chip is represented by the number of inputs of the LUT element). Next, this STG must be converted to the equivalent STT (block 2). The distribution of states over sets \(S^{0},S2,S3\) is performed in a cycle, including blocks 3-7. The distribution starts from the first state (block 3). In block 4, condition (18) is checked. If this condition is met (output \"Yes\" from block 4), then the state \(s_{m}\in S\) is placed in set \(S^{0}\) (block FC). If this condition is violated (output \"No\" from block 4), then condition (42) is checked (block 5). If this condition is met (output \"Yes\" from block 5), then the state \(s_{m}\in S\) is placed in set 53 (block FD). If this condition is violated (output \"No\" from block 5), then the state \(s_{m}\in S\) is the state \(s_{m}\in S\) is placed in set 52 (block PC). The analysis of the next state begins (block 6). If all states are distributed (output \"Yes\" from block 7), then the FSM architecture selection begins (transition to block 8).