Question

Let B = {x | x ? {a, b, c}* and x contains the same number of at least two of the three
symbols}. Show that B is a CFL by giving either a stack machine or a CFG for it.

Answer 1

The CFG for given language is as follows:

{{S,X,Y,Z,A,B,C},{a,b,c},P,S} with production rulw

S-> X|Y|Z

X-> XaXbX| XbXaX | C

Y-> YbYcY| YcYbY | A

Z-> ZaZcZ| ZcZaZ | B

A-> aA |

B-> bB |

C-> cC |

Here X will generate all strings have equal no. of 'a's and 'b's.

Here Y will generate all strings have equal no. of 'b's and 'c's.

Here Z will generate all strings have equal no. of 'a's and 'c's.

A generate strings of a.

B generate strings of b.

C generate strings of c.