Intereting Posts

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Differentiation continuous iff domain is finite dimensional
Incorrect Chain Rule Proof
Necessary/sufficient conditions for an infinite product to be exactly equal to $1$
Prove $2^{1092}\equiv 1 \pmod {1093^2}$, and $3^{1092} \not \equiv 1 \pmod {1093^2}$
Prove $\alpha \in\mathbb R$ is irrational, when $\cos(\alpha \pi) = \frac{1}{3}$
Linear optimization problem.
Wolfram Alpha can't solve this integral analytically
Calculating an Angle from $2$ points in space
Fundamental Theorem of Calculus.
Proof of uniqueness of LU factorization
Show $\lim\limits_{n\rightarrow\infty}n\left(\frac{1}{n}\sum_{i=1}^{n}f\left(\frac{i}{n}\right)-\int_{0}^{1}f(x)dx\right)=\frac{f(1)-f(0)}{2}$
Is the function $f(x)=x$ on $\{\pm\frac1n:n\in\Bbb N\}$ differentiable at $0$?
Cardinal Arithmetic Question
Extract real and imaginary parts of $\operatorname{Li}_2\left(i\left(2\pm\sqrt3\right)\right)$

Let $L = L_1 \cap L_2 $, where $L_1$ and $L_2$ are languages as defined below:

$L_1= \left \{ a^m b^mca^nb^m \mid m,n \geq 0 \right \}$

$L_2=\left \{ a^i b^j c^k \mid i,j,k \geq 0 \right \}$

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Then L is

- Not recursive
- Regular
- Context free but not regular
- Recursively enumerable but not context free.

I tried to solve $:$

$L_1 = {c, abcb, abcab, aabbcbb, …}$

$L_2 = {ϵ, a, b, c, ab, ac, bc, abc, …}$

So, $L_1 ∩ L_2 = {c}$ , which is Regular.

Is $L_1$ context free language and is my explanation correct ?

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Yes the result is correct but you don’t really say why.

If $s \in L_1$ then $s$ contains a $c$. If also $s \in L_2$ then $s = a^ib^jc^k$ so $k$ has to be $ > 0$ (in fact $k$ has to be $1$) and $s$ ends in a $c$. Because $s \in L_1$, $s=a^mb^mca^nb^m$, so $n = m = 0$ if $s$ is to end in $c$. But then $s = c$.

And clearly $c \in L_1 \cap L_2$.

So $L = L_1 \cap L_2 = \{c\}$.

Thus $L$ is regular, so only 2. is true.

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