Why does set of all strings over the alphabet {0,1} is represented by (0+1)*? As per my understanding (0+1) means either 0 and 1 and * means 0 or more occurrence of the given string. Now when we do (0+1)* it looks like we have to select either 0 or 1 and do a * on that so the resulting should be something like


but why is it following?



1 Answer 1


It is a Klenee operator and it means all number of $(0 + 1)(0 + 1)\cdots$ with all possible length. As $(0+1)^{10}$ means $(0+1)(0+1)\cdots(0+1)$ for ten times. Hence, All possible combinations of $0$ and $1$ are comming in $(0+1)^*$.

In the other words by the definition, it means the union of all $(0 + 1)^i$ for all $i$ from $0$ to $\infty$.


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