Chapter 13.1, Problem 19E

To determine

(a)

Determine whether $G=\left(V,T,S,P\right)$ is a type $0$ grammar but not a type $1$ grammar, a type $1$ grammar but not a type $2$ grammar or a type $2$ grammar but not a type $3$ grammar if the set of production is.

$S\to aAB,A\to Bb,B\to A$

To determine

(b)

Determine whether $G=\left(V,T,S,P\right)$ is a type $0$ grammar but not a type $1$ grammar, a type $1$ grammar but not a type $2$ grammar or a type $2$ grammar but not a type $3$ grammar if the set of production is.

$S\to aA,A\to a,A\to b$

To determine

(c)

Determine whether $G=\left(V,T,S,P\right)$ is a type $0$ grammar but not a type $1$ grammar, a type $1$ grammar but not a type $2$ grammar or a type $2$ grammar but not a type $3$ grammar if the set of production is.

$S\to ABa,AB\to a$

To determine

(d)

Determine whether $G=\left(V,T,S,P\right)$ is a type $0$ grammar but not a type $1$ grammar, a type $1$ grammar but not a type $2$ grammar or a type $2$ grammar but not a type $3$ grammar if the set of production is.

$S\to ABa,AB\to aB,B\to ab$

To determine

(e)

Determine whether $G=\left(V,T,S,P\right)$ is a type $0$ grammar but not a type $1$ grammar, a type $1$ grammar but not a type $2$ grammar or a type $2$ grammar but not a type $3$ grammar if the set of production is.

$S\to bA,A\to B,B\to a$

To determine

(f)

Determine whether $G=\left(V,T,S,P\right)$ is a type $0$ grammar but not a type $1$ grammar, a type $1$ grammar but not a type $2$ grammar or a type $2$ grammar but not a type $3$ grammar if the set of production is.

$S\to aA,aA\to B,B\to aA,A\to B$

To determine

(g)

Determine whether $G=\left(V,T,S,P\right)$ is a type $0$ grammar but not a type $1$ grammar, a type $1$ grammar but not a type $2$ grammar or a type $2$ grammar but not a type $3$ grammar if the set of production is.

$S\to bA,A\to b,S\to \lambda$

To determine

(h)

Determine whether $G=\left(V,T,S,P\right)$ is a type $0$ grammar but not a type $1$ grammar, a type $1$ grammar but not a type $2$ grammar or a type $2$ grammar but not a type $3$ grammar if the set of production is.

$S\to AB,B\to aAb,aAb\to b$

To determine

(i)

Determine whether $G=\left(V,T,S,P\right)$ is a type $0$ grammar but not a type $1$ grammar, a type $1$ grammar but not a type $2$ grammar or a type $2$ grammar but not a type $3$ grammar if the set of production is.

$S\to aA,A\to bB,B\to b,B\to \lambda$

To determine

(j)

Determine whether $G=\left(V,T,S,P\right)$ is a type $0$ grammar but not a type $1$ grammar, a type $1$ grammar but not a type $2$ grammar or a type $2$ grammar but not a type $3$ grammar if the set of production is.

$S\to A,A\to B,B\to \lambda$