I took my theory of computation exams a few weeks ago, and this was one of the questions:

Assume language $L=\{(a^nb^m)^r \mid n,m,r\ge 0\}$

 

Is L regular? If yes provide a regular expression or an automaton for it.

After I briefly asked him the answer after the exam, it appears it really is regular (I believe he said the expression is the simple $(a^*b^*)^*$). However I cannot seem to understand why that is. The way I see it, its concatenating $a^nb^m$ r times, like this:

$a^nb^ma^nb^ma^nb^m...a^nb^ma^nb^m$,

which isn't regular since there is no way for an automaton to recall n and m every time. Where am I at fault here?

EDIT: I talked to the professor again, he admitted it was a mistake. The language is indeed not regular.

I took my theory of computation exams a few weeks ago, and this was one of the questions:

Assume language $L=\{(a^nb^m)^r \mid n,m,r\ge 0\}$

Is L regular? If yes provide a regular expression or an automaton for it.

After I briefly asked him the answer after the exam, it appears it really is regular (I believe he said the expression is the simple $(a^*b^*)^*$). However I cannot seem to understand why that is. The way I see it, its concatenating $a^nb^m$ r times, like this:

$a^nb^ma^nb^ma^nb^m...a^nb^ma^nb^m$,

which isn't regular since there is no way for an automaton to recall n and m every time. Where am I at fault here?

EDIT: I talked to the professor again, he admitted it was a mistake. The language is indeed not regular.

I took my theory of computation exams a few weeks ago, and this was one of the questions:

Assume language L={$(a^nb^m)^r$, where n,m,r$\ge$0}

Is L regular? If yes provide a regular expression or an automaton for it.

After I briefly asked him the answer after the exam, it appears it really is regular (I believe he said the expression is the simple $(a^*b^*)^*$). However I cannot seem to understand why that is. The way I see it, its concatenating $a^nb^m$ r times, like this:

$a^nb^ma^nb^ma^nb^m...a^nb^ma^nb^m$,

which isn't regular since there is no way for an automaton to recall n and m every time. Where am I at fault here?

EDIT: I talked to the professor again, he admitted it was a mistake. The language is indeed not regular.

I took my theory of computation exams a few weeks ago, and this was one of the questions:

Assume language $L=\{(a^nb^m)^r \mid n,m,r\ge 0\}$

Is L regular? If yes provide a regular expression or an automaton for it.

After I briefly asked him the answer after the exam, it appears it really is regular (I believe he said the expression is the simple $(a^*b^*)^*$). However I cannot seem to understand why that is. The way I see it, its concatenating $a^nb^m$ r times, like this:

$a^nb^ma^nb^ma^nb^m...a^nb^ma^nb^m$,

which isn't regular since there is no way for an automaton to recall n and m every time. Where am I at fault here?

EDIT: I talked to the professor again, he admitted it was a mistake. The language is indeed not regular.

I took my theory of computation exams a few weeks ago, and this was one of the questions:

Assume language L={$(a^nb^m)^r$, where n,m,r$\ge$0}

Is L regular? If yes provide a regular expression or an automaton for it.

After I briefly asked him the answer after the exam, it appears it really is regular (I believe he said the expression is the simple $(a^*b^*)^*$). However I cannot seem to understand why that is. The way I see it, its concatenating $a^nb^m$ r times, like this:

$a^nb^ma^nb^ma^nb^m...a^nb^ma^nb^m$,

which isn't regular since there is no way for an automaton to recall n and m every time. Where am I at fault here?

I took my theory of computation exams a few weeks ago, and this was one of the questions:

Assume language L={$(a^nb^m)^r$, where n,m,r$\ge$0}

Is L regular? If yes provide a regular expression or an automaton for it.

After I briefly asked him the answer after the exam, it appears it really is regular (I believe he said the expression is the simple $(a^*b^*)^*$). However I cannot seem to understand why that is. The way I see it, its concatenating $a^nb^m$ r times, like this:

$a^nb^ma^nb^ma^nb^m...a^nb^ma^nb^m$,

which isn't regular since there is no way for an automaton to recall n and m every time. Where am I at fault here?

EDIT: I talked to the professor again, he admitted it was a mistake. The language is indeed not regular.