Finite State Automaton Language We're given these two finite state machines where the alphabet consists of ${a, b, c}$. The question is to determine the language for the following two machines. I tried following the machines to find the language, but the languages I derived are quite verbose.

FSA #1



This FSA accepts words with at least one a followed by zero or more b's or words with at least one a followed by zero or more b's followed by at least one c.

FSA #2



This  FSA accepts words with at least one a followed by at least one b or words with at least one a followed by at least one b followed by one c.

I tried converting these FSAs to regular expressions and found that my solutions hold up, but I'm wondering if there is a more concise way to explain the language of each FSA. My language explanations seem quite verbose, so any help would be appreciated.
Finite state automatons recognize regular languages. The advantage of regular languages is that it is usually trivial to express them formally.

FSA #1

$$L(M_1) = \left\{ a^kb^lc^m | k &gt; 0, l \geq 0, m \in \{ 0, 1 \} \right\}$$

FSA #2

$$L(M_2) = \left\{ a^kb^lc^m | k &gt; 0, l &gt; 0, m \in \{ 0, 1 \} \right\}$$