## 4 The Proposed Methodology--A Demonstration
### Proposed CFG to Detect L-Type Pseudoknots
\begin{table}
\begin{tabular}{c c} \hline
**Enumeration** & **Syntactic Rules** \\ \hline
64 & L \(\rightarrow\) “A” L \\
65 & L \(\rightarrow\) “U” L \\
66 & L \(\rightarrow\) “C” L \\
67 & L \(\rightarrow\) “G” L \\
68 & L \(\rightarrow\) “A” \\
69 & L \(\rightarrow\) “U” \\
70 & L \(\rightarrow\) “C” \\
71 & L \(\rightarrow\) “G” \\ \hline
72 & D \(\rightarrow\) K K \\ \hline
73 & K \(\rightarrow\) “A” \\
74 & K \(\rightarrow\) “U” \\
75 & K \(\rightarrow\) “C” \\
76 & K \(\rightarrow\) “G” \\
77 & K \(\rightarrow\)\(\epsilon\) \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._ \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c c c} \hline
**String Enumeration** & **0** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** & **15** & **16** & **17** & **18** & **19** \\ \hline
**String** & U & U & U & A & C & G & G & C & C & G & A & A & U & U & C & G & C & G & G & A \\ \hline
**Parser output**: &. &. & (. &. & [ &. &. &. & \{ & \}. &. &. &. & ] &. &. &. &. &. \\ \hline
**Step 1** &. & ( & (. &. & [ &. &. &. & \{ & \} ) &. &. &. & ] &. &. &. &. &. &. \\
**Step 2** &. & ( & ( &. &. & [ &. &. & \{ & \{ & \} ) &. &. &. & \} &. &. &. &. \\
**Step 3** &. & ( & ( &. & [ &. &. & \{ & \{ & \} &. & \}. &. & \} ] &. &. & \} & \} & \} & \} \\ \hline \end{tabular}
\end{table} 
Table 2: Locating base pairs around the core stems of a pseudoknot. \begin{table}
\begin{tabular}{c} \hline
**Platform** \\ \hline
**RNA/Dot Bracket** \\ \hline
**Ground truth** \\ \hline
**Knotity** \\
**IBrnot** \\ Knotty** \\
**Knotty** \\
**IBrnot** \\
**Knotty** \\
**C**notty** \\
**C**not** \\
The proposed approach for detecting L-type pseudoknots in RNA sequences involves utilizing syntactic pattern recognition techniques and a CFG parser. To represent RNA, the four standard nucleotide bases, i.e., adenine, cytosine, guanine, and uracil, are represented as single characters \"A\", \"C\", \"G\", and \"U\", respectively, and any RNA can be linguistically represented as a string of these symbols. The proposed grammar, \(G_{Lpsendo}\), consists only of these four terminal symbols, and it includes four non-terminal symbols in the set NT = \(\{S,L,D,K\}\). The syntactic rules for the \(G_  
identify a potential pseudoknot in the input string. The L-type pseudoknot is defined as having at least three base pairs, forming intercalated core stems. The non-terminal symbol L generates sequences of bases that make up the four interior loops of the pseudoknot, while the non-terminal symbol D generates sequences of bases between the two main crossing base pairs. The CFG parser can identify pseudoknots in strings that have their initial and final symbols belonging to the core stems group, but it can also operate effectively on substrings using the sliding windows technique. The approach involves parsing all substrings of the sequence, starting from the shortest one that commences with the first symbol of the sequence and increasing the length by one symbol until the entire RNA sequence is included. The parsing operation stops when the substring length falls below a specified threshold, corresponding to the minimum length of the pseudoknot. To handle the grammatical ambiguity, YAEP, a highly efficient parser that utilizes [PERSON]'s algorithm, is selected for the CFG parser. A context-free grammar is used to enable the expansion with attributes, which can store probabilities and facilitate the pruning of parse trees while constructing them, as a forthcoming extension. An alternate method for the initial task using a brute force approach was also proposed to improve the system's performance. The proposed system allows the user to adjust the grammar to choose whether or not to include U-G base pairs in the loops of the pseudoknot. Furthermore, the proposed approach can be extended to incorporate longer substrings between the crossing base pairs with appropriate modifications to the grammar.