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Accepted

### Why $(a+b)^* = (a^*b)^* a^*$

Consider any string $\omega$ that belongs to $(a+b)^*$. Now suppose $\omega$ contains $n$ number of $b$s. We can now partition $\omega = x_1 x_2 \dots x_n y$, where all $x_i$ are of the form $a^*b$ ...
• 1,390

### Why $(a+b)^* = (a^*b)^* a^*$

Every b in a string belonging to (a+b)* is preceded by 0, 1, 2 or more a's. And the last b is followed by 0, 1, 2 or more a's.
• 30.6k
Accepted

### Question about a grammar who generates $(0+1)^*$

We can prove this using mathematical induction. For base case, it is easy to see that $S$ can generate $\varepsilon, 0, 1, 00, 11, 01, 10$. Now we assume $S$ can generate any binary string on $0$s and ...
• 1,390

### Why $(a+b)^* = (a^*b)^* a^*$

Just as a comment, it's also possible to show this purely algebraically, using Kozen's axioms for Kleene algebra. To show that: $$\displaystyle x^*\le y$$ It is sufficient to show that: \...
• 22.3k

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