Why can finite-state grammars not fully describe English sentence structure?

In automata theory, finite-state grammars are restricted to generating regular languages, which lack the descriptive power necessary to account for the complex phrase structure of natural languages like English.1

These grammars are inadequate for several key reasons:

• Inability to handle recursion: Finite-state grammars cannot generate self-embedded structures, such as the sentence "the man the dog bit ran away," which require recursive operations to nest phrases within one another.12
• Lack of structural depth: They cannot account for sentences with multiple interpretations, such as "she is a pretty little girl," because they cannot represent the hierarchical relationships between words and phrases.1
• Limited memory: Because finite-state acceptors read symbols sequentially without the ability to store and retrieve complex structural information, they cannot model the long-distance dependencies and nested constituents that are fundamental to human language.1

To achieve descriptive adequacy, linguists employ more sophisticated systems, such as transformational-generative grammar, which utilize recursive rules to produce an infinite variety of grammatical structures from finite means.2