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How to find regular expression using ardent's rule for recursive expressions?

The correct equation system is the following: $A=0A+1B$ $B=0B+1A+\epsilon$ Hence using Arden lemma, you obtain $B=0^*(1A+\epsilon)$ replacement in $A$ equation gives: $A=0A+10^*(1A+\epsilon)$ $A=0A+...
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