i am having trouble understanding this concept. would really appreciate your corrections so i could learn and improve.
1)$L=\left\{w\:\in \Sigma^* |\:w\:begins\:and\:ends\:with\:aa\right\}$
2)$L=\Sigma^* \:-\:\left(\left\{\epsilon ,\:a\:,b\right\}\:\cup \left\{bba^i|\:i\:\ge 0\right\}\right)$
(both are over $\Sigma = {a,b,c}$, but different problems
i don't understand this, but i'll try anyway:
1)equivalence classes:
$S_1 = (b+c)\Sigma ^*$
$S_2 = \epsilon$
$S_3 = aa + aa\Sigma^*aa$ (i think there's a mistake here)
$S_4 = aa \Sigma^*(b+c)$
2)i really don't know, but i'll try anyway:
$S_1 = \epsilon$
$S_2 = a$
$S_3 = b$
$S_4 = bba*$
(i don't know how to do $S_5$, would really appreciate your help with it).
tried to do my best, even though i know i've had errors and mistakes there. please show me the right way so i could learn what i've done wrong.
thank you very much.
side question if possible: how can i find the words that separate between the equivalence classes? thank you very much for your help