reverse - Context-free grammar and Reversal -

i'm designing context-free grammar generate language:

{ w in {a,b}* | w of form uvu^r, u , v strings in {a,b}* }

i define first 2 strings as:

u -> au | bu | _ v -> av | bv | _

and combine those:

s -> uv

but how express reversal context-free grammar?

you need make use of context-free-ness of grammar (what you're presenting far regular grammar):

u-> aua | bub | | b | _

will match things "ababa" , "aabaa", not "aabba".

i'll leave alter needs - keep in mind specified language has possibility of u being empty string, hence generates strings in {a,b}*.

TY