Context-Free Grammars

This lecture introduces context-free grammars as a formalism more expressive than finite automata and regular expressions, allowing the description of context-free languages. The instructor explains the equivalence between pushdown automata and context-free grammars, detailing the components and transitions of pushdown automata. The lecture covers the definition of context-free grammars, including terminals, non-terminals, and rules. It explores the concept of context-free languages and how to verify if a word belongs to a grammar's language using algorithms like the CYK algorithm. Additionally, the lecture delves into the pumping lemma for context-free languages, demonstrating how to find a repeated substring within a language. The hierarchy of grammar types is discussed, highlighting the restrictions and expressiveness of different grammar levels, leading up to Type 0 grammars, which have no restrictions on rule application.