Testbook Test Series: Theory of Computation - Identify Class Language

Question

Doubt 1:

according to me L1 should be subset of L2. But answer is d) L1,L2,L3 are incomparable. Please explain this question to me

 

 

Doubt 2:

which type of language is L4?

Comments

Doubt 1:

L1 should be subset of L2 for a,b,c and not for d

for 'd' L2 is a subset of L1

Doubt 2:

Anything with Kleen closer is regular

regular.CSL=CSL

Answer 1

Q(1)  L1={$\varepsilon$,abcd,abcdd,aabbccdd,aabbccdddd,aabbccdddd,........}

L2={$\varepsilon$,aabbccd,aabbccdd,aaaabbbbccccd,aaaabbbbccccdd.........}

L3={$\varepsilon$,aabbcdd,aabbcccdd,................}

how can we say that$L2\subseteq L1$ or $L1\subseteq L2$ if it does then all the language generated by L2 must be in L1 or all the language which is generated by L1 must be in L1 but we can see all are generating different except some of string .

 

Q(2) it will be CSL

Comments

for question 2 I also think it is CSL but answer given was Regular language.

---

any explanation given?

---

No. only answer is given

---

Doubt 2 

L4 must be regular.

Answer 2

Doubt 2 

L4 must be regular.