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Im having a lot of trouble proving that for the Regular expression $R_{1} = \left( a^{*} b^{*} \right)^{*}$ and $R_{2} = \left( a+b \right)^{*}$ that $L \left( R_{1} \right) = L \left( R_{2} \right)$. I was wondering if anyone could help me with this? thanks

Blanco
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2 Answers2

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Proving equivalence of regular expressions can be tedious, so let me recommend two different strategies.

  1. Convert both expressions into regular grammars using the algorithm from the equivalence proof. Then prove them equivalent.

  2. Even more mechanical: convert both expressions into finite automata (using the algorithm from the equivalence proof). Showing equivalence is now moslty an algorithmic task the solution for which you should have seen in class.

    Determinise, minimize, show that they are isomorphic.

Raphael
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First prove that every word in R1 is also in R2; then prove that every word in R2 is also in R1. Spend some time on each and see what progress you can make.

D.W.
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