Problem Detail: I just started a course called ‘Automata and Formal Languages’. I’m having difficulty in proofingdisproofing this equality. $ (L_{1} circ L_{2})^{+} = L_{1}^{+} circ L_{2}^{+} $ Where: $ L_{1} $, $L_{2}$ are Languages. $circ$ is the concatenation operation between two languages. $+$ is the Kleene plus closure defined by $bigcup _{i = 1}^{infty }L^{i} $ I tried finding a counter example and also tried to formally proof but had no luck. Can someone please point me in the correct direction?
Asked By : elmekiesIsrael
Answered By : Yuval Filmus
Let’s use $A$ for $L_1$ and $B$ for $L_2$. If you unpack both sides, you get $$ (AB)^+ = AB + ABAB + ABABAB + cdots A^+B^+ = AB + AAB + ABB + AABB + cdots $$ Perhaps this can give you some ideas.
Best Answer from StackOverflow
Question Source : http://cs.stackexchange.com/questions/32509
