## 2 Related Work
### Context-Free Grammar (CFG)  
[PERSON] (2014) introduced in the fifties of the last century a new theory to describe the grammar of natural and formal languages. The described grammar is ordered in a hierarchy and the most popular type of this hierarchy is context-free grammar. Figure 1A shows such a context-free grammar, which can parse the following sentence: \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Parser** & **“Real” Sent.** & **Type** & **Training** & **Dataset** & **POS** & **M/S** & **Case** \\ \hline Bubble Parser & (Yes) 50\% & Logical & No & German G. & Yes & Yes & Yes \\ Stanford parser & Yes & Logical/Statistical & Yes & Treebanks & Yes & Partly & No \\ Constraint Grammar & No & Logical & No & Rule-Set & No & No & No \\ SpaCy & Yes & Statistical & Yes & Treebanks & Yes & No & No \\ Large Language Model & Yes & Statistical & Yes & Raw Texts & Yes & Yes & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of parsing methods (Abbreviations: sent. = sentences; G. = grammar; M/S = main-/sub-clause; POS = part of speech). The grammar consists of non-terminal and terminal rules. The symbol on the left in each rule is replaced by the symbols on the right in an iterative process. On the left side, there always occurs a non-terminal symbol, which can be treated as non-final. A terminal symbol is final because it cannot be replaced anymore and constitutes a word in the derived sentence. The starting point in this parse process is a single non-terminal symbol S. In the example grammar shown in Figure 1A, the starting symbol S can solely be replaced by the non-terminal symbols NP and VP. The symbol NP can solely be replaced by the non-terminal symbols DT and N, whereas the symbol VP is replaced by the non-terminal symbol V. Using the terminal rules, shown in Figure 1A, one obtains the desired sentence. The grammar rules in Figure 1A are very simple and solely allow one to parse a single sentence because one has no choice in the replacing process. Usually, the given context-free grammar allows choices and often parses infinitely many sentences. The Cocke-Younger-Kasami Algorithm (CYK algorithm) [15] was invented for context-free grammars to reverse this derivation. The algorithm starts with a given sentence and treats all words as terminal symbols of a specific context-free grammar. The algorithm reverses the grammar rules to return to the starting symbol S. The replacing rules then describe a parse tree as shown in Figure 1A. Context-free grammar is commonly employed to describe formal languages, such as programming languages. However, it has not yet been possible to develop a comprehensive rule system for any natural language using this method. As a result, context-free grammar is limited to parsing simplified examples rather than actual sentences from natural languages. Probabilistic Context-Free Grammar (PCFG)  
Context-free grammar parsing often results in multiple possible derivations for a single sentence due to the numerous options available for replacing non-terminal symbols. Probabilistic context-free grammar addresses this ambiguity by assigning a probability to each replacement rule. Consequently, the derivation of a sentence is associated with  
Figure 1: Illustration of four alternative parsing methods. (**A**) Context-free grammar parses the sentence “The dog laughs”. (**B**) Constraint grammar parses the sentence “Time flies like an arrow”. (**C**) Dependency parsing parses the sentence “Time flies like an arrow”. (**D**) Large language model parses the sentence “Time flies like an arrow”. a probability, calculated as the product of the probabilities of all the replacement rules applied in the derivation. The most likely parse is determined as the one with the highest probability. Figure 1A illustrates (arbitrary) example probabilities (shown in brackets) assigned to various replacement rules. We compare our parser with the Stanford probabilistic context-free grammar parser [11] (CoreNLP version 4.2.1).