Question

Please help with the following context free grammar over alphabet (0,1):

S —> A | B

A —> 1S | ^

B—> 0S | ^

a. Show that the grammar is ambiguous for a non-empty string.

b. Convert the CFG to Chomsky normal Form.

Answer 1

a)String is 1

leftmost derivation i)

S->A

->1S

->1A

->1

leftmost derivation ii)

S->A

->1S

->1B

->1

two leftmost derivations for string 1

so the grammar is ambigous.

b)

S —> A becomes

S->AX

X-> ^

S->B becomes

S->BX

A->1S becomes

A->YS

Y->1

A->^ is same

B->0S becomes

B->ZS

Z->0

B->^ is same

chomsky normal form is

S->AX

X-> ^

S->BX

A->YS

Y->1

A->^

B->ZS

Z->0

B->^