Understanding Chomsky Normal Form in Context-Free Grammars Chomsky Normal Form (CNF) is a specific structure for context-free grammars (CFGs), where productions are either of the form A → BC or A → a. In CNF, each production's left-hand side contains one non-terminal and the right-hand side can contain two non-terminals or one terminal. To convert an existing CFG into CNF, it’s essential to simplify the grammar by eliminating useless symbols, epsilon productions, and unit productions before proceeding with replacements.
Transforming Grammar Productions into Valid CNFs To transform a given CFG into CNF effectively involves replacing terminals on the right-hand sides of productions with new non-terminals while ensuring that all resulting forms adhere to CNF rules. For example, if 'S' produces 'BA', we replace B and A with corresponding new variables like C1 and C2 respectively until every production fits within defined structures of either two non-terminals or one terminal per rule. The final output consists solely of valid transformations that maintain grammatical integrity under Chomsky normal standards.