Convert chomsky normal form into binary form, Theory of Computation

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.

Posted Date: 3/9/2013 1:52:37 AM | Location : United States







Related Discussions:- Convert chomsky normal form into binary form, Assignment Help, Ask Question on Convert chomsky normal form into binary form, Get Answer, Expert's Help, Convert chomsky normal form into binary form Discussions

Write discussion on Convert chomsky normal form into binary form
Your posts are moderated
Related Questions

We will assume that the string has been augmented by marking the beginning and the end with the symbols ‘?' and ‘?' respectively and that these symbols do not occur in the input al

distinguish between histogram and historigram

Another striking aspect of LTk transition graphs is that they are generally extremely ine?cient. All we really care about is whether a path through the graph leads to an accepting


Since the signi?cance of the states represented by the nodes of these transition graphs is arbitrary, we will allow ourselves to use any ?nite set (such as {A,B,C,D,E, F,G,H} or ev

As de?ned the powerset construction builds a DFA with many states that can never be reached from Q′ 0 . Since they cannot be reached from Q′ 0 there is no path from Q′ 0 to a sta

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

Find the Regular Grammar for the following Regular Expression:                    a(a+b)*(ab*+ba*)b.