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To say that a context-free grammar is in Greibach normal form (GNF) means that all production rules are of the form:
- <math>A \to \alpha X<math>
where A is a nonterminal symbol, α is a terminal symbol and X is (possibly empty) sequence of nonterminal symbols.
No grammar in GNF can generate the null string. Conversely, every context-free grammar which does not generate the null string can be transformed into an equivalent grammar in Greibach normal form. This can be used to prove that every context-free language can be accepted by a non-deterministic pushdown automaton.
Greibach normal form is named for Sheila Greibach.
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