5 typo (loret ipsum..), singular

I am struggling with this question for a very long time and just can't find the flaw. So I am given a false Theorem:

The language $$\{awwa \mid w \in \{a,b\}^* \}$$ is regular.

Well, that part is obvious, we can prove itthat the language is not regular using the pumping lemma.

The question I am asked is to find the flaw in the "proof" for this theorem:

Let

$$\qquad L_1 = \{ aw \mid w \in \{a,b\}^* \}$$

$$\qquad L_1^R = \{ aw \mid w \in \{a,b\}^* \}$$$$\qquad L_1^R = \{ wa \mid w \in \{a,b\}^* \}$$

Let $$L_2 = L_1 L_1^R = \{ awwa \mid w \in \{a,b\}^*\}$$ be even-length palindromes that begin and end with an $$a$$. Since $$L_1$$ is regular, and the class of regular languages is closed under reversal and concatenation, we conclude $$L_2$$ is also regular.

Can you find the flaw? I could build a DFA for $$L_1$$ and $$L_1^R$$, so I know they are regular. And regular languages are closed under reversal and concatenation.

But, however, $$L_2$$ is still not regular, so where is the mistake in the "proof"?

I am struggling with this question for a very long time and just can't find the flaw. So I am given a false Theorem:

The language $$\{awwa \mid w \in \{a,b\}^* \}$$ is regular.

Well, that part is obvious, we can prove it using the pumping lemma.

The question I am asked is to find the flaw in the "proof" for this theorem:

Let

$$\qquad L_1 = \{ aw \mid w \in \{a,b\}^* \}$$

$$\qquad L_1^R = \{ aw \mid w \in \{a,b\}^* \}$$

Let $$L_2 = L_1 L_1^R = \{ awwa \mid w \in \{a,b\}^*\}$$ be even-length palindromes that begin and end with an $$a$$. Since $$L_1$$ is regular, and the class of regular languages is closed under reversal and concatenation, we conclude $$L_2$$ is also regular.

Can you find the flaw? I could build a DFA for $$L_1$$ and $$L_1^R$$, so I know they are regular. And regular languages are closed under reversal and concatenation.

But, however, $$L_2$$ is still not regular, so where is the mistake in the "proof"?

I am struggling with this question for a very long time and just can't find the flaw. So I am given a false Theorem:

The language $$\{awwa \mid w \in \{a,b\}^* \}$$ is regular.

Well, that part is obvious, we can prove that the language is not regular using the pumping lemma.

The question I am asked is to find the flaw in the "proof" for this theorem:

Let

$$\qquad L_1 = \{ aw \mid w \in \{a,b\}^* \}$$

$$\qquad L_1^R = \{ wa \mid w \in \{a,b\}^* \}$$

Let $$L_2 = L_1 L_1^R = \{ awwa \mid w \in \{a,b\}^*\}$$ be even-length palindromes that begin and end with an $$a$$. Since $$L_1$$ is regular, and the class of regular languages is closed under reversal and concatenation, we conclude $$L_2$$ is also regular.

Can you find the flaw? I could build a DFA for $$L_1$$ and $$L_1^R$$, so I know they are regular. And regular languages are closed under reversal and concatenation.

But, however, $$L_2$$ is still not regular, so where is the mistake in the "proof"?

4 fix a typo

I am struggling with this question for a very long time and just can't find the flaw. So I am given a false Theorem:

The language ${awwa \mid w \in {a,b}^* }%$$\{awwa \mid w \in \{a,b\}^* \}$$ is regular. Well, that part is obvious, we can prove it using the pumping lemma. The question I am asked is to find the flaw in the "proof" for this theorem: Let $$\qquad L_1 = \{ aw \mid w \in \{a,b\}^* \}$$ $$\qquad L_1^R = \{ aw \mid w \in \{a,b\}^* \}$$ Let $$L_2 = L_1 L_1^R = \{ awwa \mid w \in \{a,b\}^*\}$$ be even-length palindromes that begin and end with an $$a$$. Since $$L_1$$ is regular, and the class of regular languages is closed under reversal and concatenation, we conclude $$L_2$$ is also regular. Can you find the flaw? I could build a DFA for $$L_1$$ and $$L_1^R$$, so I know they are regular. And regular languages are closed under reversal and concatenation. But, however, $$L_2$$ is still not regular, so where is the mistake in the "proof"? I am struggling with this question for a very long time and just can't find the flaw. So I am given a false Theorem: The language${awwa \mid w \in {a,b}^* }% is regular.

Well, that part is obvious, we can prove it using the pumping lemma.

The question I am asked is to find the flaw in the "proof" for this theorem:

Let

$$\qquad L_1 = \{ aw \mid w \in \{a,b\}^* \}$$

$$\qquad L_1^R = \{ aw \mid w \in \{a,b\}^* \}$$

Let $$L_2 = L_1 L_1^R = \{ awwa \mid w \in \{a,b\}^*\}$$ be even-length palindromes that begin and end with an $$a$$. Since $$L_1$$ is regular, and the class of regular languages is closed under reversal and concatenation, we conclude $$L_2$$ is also regular.

Can you find the flaw? I could build a DFA for $$L_1$$ and $$L_1^R$$, so I know they are regular. And regular languages are closed under reversal and concatenation.

But, however, $$L_2$$ is still not regular, so where is the mistake in the "proof"?

I am struggling with this question for a very long time and just can't find the flaw. So I am given a false Theorem:

The language $$\{awwa \mid w \in \{a,b\}^* \}$$ is regular.

Well, that part is obvious, we can prove it using the pumping lemma.

The question I am asked is to find the flaw in the "proof" for this theorem:

Let

$$\qquad L_1 = \{ aw \mid w \in \{a,b\}^* \}$$

$$\qquad L_1^R = \{ aw \mid w \in \{a,b\}^* \}$$

Let $$L_2 = L_1 L_1^R = \{ awwa \mid w \in \{a,b\}^*\}$$ be even-length palindromes that begin and end with an $$a$$. Since $$L_1$$ is regular, and the class of regular languages is closed under reversal and concatenation, we conclude $$L_2$$ is also regular.

Can you find the flaw? I could build a DFA for $$L_1$$ and $$L_1^R$$, so I know they are regular. And regular languages are closed under reversal and concatenation.

But, however, $$L_2$$ is still not regular, so where is the mistake in the "proof"?

3 edited tags

# a A flawed theorem -about regular languages

I am struggling with this question for a very long time and just can't find the flaw...Please help me figure it out.. So So I am given a false Theorem: "The language {awwa | w E {a

The language ${awwa \mid w \in {a,b}^* }% is regular. Well,b}* } is regular" Well...That that part is obvious , we can prove it using the pumping lemma. The question I am asked is to find the flaw in the "proof" for this theorem. So there is the "proof" for the false theorem I just mentioned. L1 = { aw | w E {a,b}* } L1R = {wa | w E (a,b)* } Let L2 = L1L1R = { awwa | w E {a,b}* } be even-length palindromes that begin and end with an a. Since L1 is regular, and the class of regular languages is closed under reversal and concatenation, we conclude L2 is also regular.: Let $$\qquad L_1 = \{ aw \mid w \in \{a,b\}^* \}$$ $$\qquad L_1^R = \{ aw \mid w \in \{a,b\}^* \}$$ Let $$L_2 = L_1 L_1^R = \{ awwa \mid w \in \{a,b\}^*\}$$ be even-length palindromes that begin and end with an $$a$$. Since $$L_1$$ is regular, and the class of regular languages is closed under reversal and concatenation, we conclude $$L_2$$ is also regular. CouldCan you find the flaw?!! I could build a dfaDFA for L1$$L_1$$ and L1R$$L_1^R$$, so I know they are regular. andAnd regular languages are closed under reversal and concatenation... But But, however, L2$$L_2$$ is still not regular, so where is the mistake in the "proof". Thank you so much for who ever try to help me !? # a flawed theorem - regular languages I am struggling with this question for a very long time and just can't find the flaw...Please help me figure it out.. So I am given a false Theorem: "The language {awwa | w E {a,b}* } is regular" Well...That part is obvious , we can prove it using the pumping lemma. The question I am asked is to find the flaw in the "proof" for this theorem. So there is the "proof" for the false theorem I just mentioned. L1 = { aw | w E {a,b}* } L1R = {wa | w E (a,b)* } Let L2 = L1L1R = { awwa | w E {a,b}* } be even-length palindromes that begin and end with an a. Since L1 is regular, and the class of regular languages is closed under reversal and concatenation, we conclude L2 is also regular. Could you find the flaw?!! I could build a dfa for L1 and L1R, so I know they are regular. and regular languages are closed under reversal and concatenation... But, however, L2 is still not regular, so where is the mistake in the "proof". Thank you so much for who ever try to help me ! # A flawed theorem about regular languages I am struggling with this question for a very long time and just can't find the flaw. So I am given a false Theorem: The language${awwa \mid w \in {a,b}^* }% is regular.

Well, that part is obvious, we can prove it using the pumping lemma.

The question I am asked is to find the flaw in the "proof" for this theorem:

Let

$$\qquad L_1 = \{ aw \mid w \in \{a,b\}^* \}$$

$$\qquad L_1^R = \{ aw \mid w \in \{a,b\}^* \}$$

Let $$L_2 = L_1 L_1^R = \{ awwa \mid w \in \{a,b\}^*\}$$ be even-length palindromes that begin and end with an $$a$$. Since $$L_1$$ is regular, and the class of regular languages is closed under reversal and concatenation, we conclude $$L_2$$ is also regular.

Can you find the flaw? I could build a DFA for $$L_1$$ and $$L_1^R$$, so I know they are regular. And regular languages are closed under reversal and concatenation.

But, however, $$L_2$$ is still not regular, so where is the mistake in the "proof"?

2 edited tags