hello,
i’ve just solved 2 questions among many, but i’m not sure i’ve got to the right result. could you check if i did it correctly(especially 2) as it’s more complicated). both are over $\Sigma = \{a,b,c\}$
1)$ L=\bigg\{w\in \sum^*\bigg| w\quad \text{starts and ends with} \quad aa\bigg\}$
the equivalence classes $R_L$ i found are:
$S_1 = \epsilon$
$S_2 = a$
$S_3 = (b+c)\sum^*+a(b+c)\sum^*$
$S_4 = aa+aaa+aa\sum^*aa$
$S_5 = aa\sum^*(b+c)a$
$S_6 = aa\sum^*(b+c)$
2)$L=\{\sum^*-(\{\epsilon, a,b\}\cup \{bba^i|i\ge 0\})\}$ ( more tricky)
after joining the sets i got that $\{\epsilon, a,b\}\cup \{bba^i|i\ge 0\}=\{\epsilon, a,b,bba^*\}$, so the equivalence classes are:
$S_1 = \epsilon$
$S_2 = a$
$S_3 = b$
$S_4 = bba*$
$S_5 = c\Sigma^*+a\Sigma^++b(a+c)\Sigma^*+bb\Sigma^*(b+c)\Sigma^*$
one thing i don’t know how to do is how to find the separating words between the equivalence classes. could you help me with that please?
thank you very much for your help, really hoping i did it correctly.
