Consider the following two finite automata. accepts and accepts . Which one of the following is TRUE?

Question

My Approach: Using Ardens Theorem I got these Regular Expressions

M1 Regular Expression R1: $(0+10)\*11(0+1)\*$ M2 Regular Expression R2: $(0+1)\*11(0+1)\*$

Answer is L1=L2

How Can we Prove That R1 generate the Same language as R2?

Answer 1

I've never studied this, so my notation may be off, but...

$L_1 \subseteq L_2$ should be apparent. To see $L_2 \subseteq L_1,$ choose any word $\in L_2$ and note the subword preceding the first instance of $11$ is generated by $(0 + 10)*$