I need to give nondeterministic finite automata for the following language: $$ L = \{w \in \{a, b\}^∗ \mid w \in ba^*a \cup ((a \cup bb)^*ab^*)\} $$ The * above are Kleene Stars
I'm having trouble reading this, I think its:
Language $L$ is a set of strings, such that each string $w$ is of the form: Zero or more $ba$, then $a$, then zero or more $abb$, then zero or more $ab$.
Is this right, if not where have I gone wrong?
Thanks.
You seem to be ignoring the $\cup$s, which I gather means "or". Plus, I think you're interpreting the $^*$s incorrectly.
If $w \in L$, then $w$ may be of the form $ba^*a$, or it may be of the form $(a \cup bb)^*ab^*$. The former is $b$ followed by one or more $a$s. Otherwise, it is zero or more instances of $a$ or $bb$ repeated (e.g. $aaabbabbbbbba$), followed by another $a$, then by zero or more $b$s.