Question

When is the grammar said to be in Chomsky Normal Form (CNF). Convert the
given grammar to CNF by showing step by step.
{ S->VP
VP->Verb
VP-> Verb VP
NP->N NP PP
Verb->climb|lift|read
N-> Tom | apple}

Answer 1

In formal language theory, a grammar is said to be in chomsky normal form (CNF) if all its rules are in the following form:

A -> BC

A -> a

S -> e

Where A,B and C are non terminal symbols , letter 'a' has a constant value , S is the start symbol and e is an empty string.

Every grammar in CNF is context free and every context free grammar can be converted into an equivalent one which has a size not greater than original grammar's size square.

To convert a given grammar into CNF there are following steps:-

• Eliminate start symbole S from right hand side of given grammar and create new production as:

S0 -> S, where S0 is new start symbol

• If given grammar contains null, unit or useless productions eliminate them.

• Eliminate constants from right side if ther exist with other constant or non termonal symbols.

• If right side of grammar has more than two non terminals eliminate them.

Answer 2

In formal language theory, a grammar is said to be in chomsky normal form (CNF) if all its rules are in the following form:

A -> BC

A -> a

S -> e

Where A,B and C are non terminal symbols , letter 'a' has a constant value , S is the start symbol and e is an empty string.

Every grammar in CNF is context free and every context free grammar can be converted into an equivalent one which has a size not greater than original grammar's size square.

To convert a given grammar into CNF there are following steps:-

• Eliminate start symbole S from right hand side of given grammar and create new production as:

S0 -> S, where S0 is new start symbol

• If given grammar contains null, unit or useless productions eliminate them.
• Eliminate constants from right side if ther exist with other constant or non termonal symbols.
• If right side of grammar has more than two non terminals eliminate them.