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Suppose G = (N, Σ, P, S) is a reduced grammar (we can certainly reduce G if we haven't already). Our algorithm is as follows:
1. Define maxrhs(G) to be the maximum length of the right hand side of any production.
2. While maxrhs 3 we convert G to an equivalent reduced grammar G' with smaller maxrhs.
3. a) Choose a production A → α where is of maximal length in G.
b) Rewrite α as α1α2 where |α1| = |α1|/2 (largest integer ≤ |α1|/2) and |α2| = |α2|/2 (smallest integer ≥ |α2|/2)
c) Replace A -> α in P by A -> α1B and B -> α2
If we repeat step 3 for all productions of maximal length we create a grammar G' all of whose productions are of smaller length than maxrhs.
We can then apply the algorithm to G' and continue until we reach a grammar that has maxrhs ≤ 2.
A context free grammar G = (N, Σ, P, S) is in binary form if for all productions A we have |α| ≤ 2. In addition we say that G is in Chomsky Normaml Form (CNF) if it is in bi
how to convert a grammar into GNF
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