What is the regex of the following FSA?

Question

This is the set of all strings that are accepted which are not 00 or 11.

I really don't see a way to have an equation for this.

The first regex part is $(0+1)$, but what then?

Also, the $\phi$ is just a dead state.

Answer 1

Strings ending at $q_1$: $1(01)^*+(01)^*=(1+\lambda)(01)^*$

Strings ending at $q_3$: $0(10)^*+(10)^*=(0+\lambda)(10)^*$

So one regex is $$(\lambda+1)(01)^*+(\lambda+0)(10)^*$$

Answer 2

I hope it can help you

$L=\{ w \in \{0,1\}^* | w $ does not contain neither of the substrings $11$ and $00$. }

a regular expression for L is: $\epsilon + 0(10)^*(1+\epsilon)+1(01)^*(0+\epsilon)$

1. $\epsilon \qquad\qquad\qquad:\text{empty string}$
2. $ 0(10)^*(1+\epsilon)\quad\,\,\,: \text{string starts with 0}$
3. $1(01)^*(0+\epsilon)\quad\,\,\,:\text{string starts with 1}$

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another regular expression is: $(0+\epsilon)(10)^*(1+\epsilon)$