I'm studying formal languages and automata, and on the section of learning how to find productions that generates the grammer, I've done some exercises pretty well and was able to do some of the exercises on the format:

$L(G_1) = \{wcw^r / w\, is\, on\, \{0,1\}^*\}$

Where $w^r$ is the reverse word, and whose productions are:

$S \rightarrow c\, / \,0S0\,/\, 1S1$

But I'm struggling to find productions of this exercise (maybe a difficult one?):

$L(G_1) = \{ww / w\, is\, a\, word\, from\, \{a,b\}^*\}$

Almost every type of production that I tried ended up generating $ww^r$ instead of $ww$ such as:

$S \rightarrow aAa\,/\,bAb$

$A \rightarrow S\,/\, \epsilon$

Is there some kind of production that I'm not considering?

EDIT: It's required to be a CSG

I'm studying formal languages and automata, and on the section of learning how to find productions that generates the grammar, I've done some exercises pretty well and was able to do some of the exercises on the format:

$L(G_1) = \{wcw^r / w\, is\, on\, \{0,1\}^*\}$

Where $w^r$ is the reverse word, and whose productions are:

$S \rightarrow c\, / \,0S0\,/\, 1S1$

But I'm struggling to find CSG of the following language (maybe a difficult one?):

$L(G_1) = \{ww / w\, is\, a\, word\, from\, \{a,b\}^*\}$

Almost every type of production that I tried ended up generating $ww^r$ instead of $ww$ such as:

$S \rightarrow aAa\,/\,bAb$

$A \rightarrow S\,/\, \epsilon$

Is there some kind of production that I'm not considering?

I'm studying formal languages and automata, and on the section of learning how to find productions that generates the grammer, I've done some exercises pretty well and was able to do some of the exercises on the format:

$L(G_1) = \{wcw^r / w\, is\, on\, \{0,1\}^*\}$

Where $w^r$ is the reverse word, and whose productions are:

$S \rightarrow c\, / \,0S0\,/\, 1S1$

But I'm struggling to find productions of this exercise (maybe a difficult one?):

$L(G_1) = \{ww / w\, is\, a\, word\, from\, \{a,b\}^*\}$

Almost every type of production that I tried ended up generating $ww^r$ instead of $ww$ such as:

$S \rightarrow aAa\,/\,bAb$

$A \rightarrow S\,/\, \epsilon$

Is there some kind of production that I'm not considering?

I'm studying formal languages and automata, and on the section of learning how to find productions that generates the grammer, I've done some exercises pretty well and was able to do some of the exercises on the format:

$L(G_1) = \{wcw^r / w\, is\, on\, \{0,1\}^*\}$

Where $w^r$ is the reverse word, and whose productions are:

$S \rightarrow c\, / \,0S0\,/\, 1S1$

But I'm struggling to find productions of this exercise (maybe a difficult one?):

$L(G_1) = \{ww / w\, is\, a\, word\, from\, \{a,b\}^*\}$

Almost every type of production that I tried ended up generating $ww^r$ instead of $ww$ such as:

$S \rightarrow aAa\,/\,bAb$

$A \rightarrow S\,/\, \epsilon$

Is there some kind of production that I'm not considering?

EDIT: It's required to be a CSG