Final answer:
To convert a grammar to CNF or GNF, you must rewrite its productions to fit specific formats. CNF requires productions to be either A → BC or A → a, and GNF requires them to be A → aX, eliminating left recursion and restructuring as needed.
Step-by-step explanation:
To convert a grammar to Chomsky Normal Form (CNF) and Greibach Normal Form (GNF), you need to apply a set of transformation rules to ensure that the productions of the grammar fit certain formats.
For CNF, every production must be of the form A → BC or A → a, where A, B, and C are nonterminal symbols and a is a terminal symbol. If we're starting with a grammar that includes productions which do not conform to this template, we'll need to introduce new nonterminals and rewrite the productions to remove any immediate left recursion, as well as break down any right-hand sides that have more than two nonterminals to fit the CNF template.
Similarly, for GNF, all productions should have the form A → aX, where A is a nonterminal, a is a terminal, and X is a string of nonterminals (possibly empty). Productions in GNF start with a terminal symbol and are followed by any number of nonterminals. Converting to GNF usually involves eliminating left-recursion and factoring the grammar to fit the required form for GNF.