Finite Automata Regular Expression

Question

Problem 1 : what is the Language associated with this regular expression ?  a*b* write it down.

Problem 2: Does either a subset or Super-set of a regular language is always a regular ?

Problem 3 : What is the difference between a^n b^n and a*b*

Explain with a example .

Comments

thanks to all who helped me .and its hard to choose best everyone is best here ...

Answer 1

problem1: language :a*b* means any no. of a's followed by any no. of  b's 

problem2:  subset or Super-set of a regular language is  not always a regular

for example 1: a*b* is a regular language but its subset a^nb^n is not regular.

for example 2:a^n  n>1 is regular whereas its superset a^n +a^nb^n is not regular

problem-3 a*b* means any no. of a followed by any no. b

    whereas a^nb^n means equal no. of a's  followed by equal no. of b's

Comments

why this a*b* is a subset of this a^nb^n .ok you know why ?but i am confused why ?i dont know.

Answer 2

(1) L={null ,a ,b,aab,aaab,................}

 L=Any number of a followed by any numbers of b

(2) Let us consider regular language L=0*1*

  For example, 0^*1^* is regular, but its subset {Oⁿ1ⁿ : n >= 0} is not regular, but its subset {01, 0011, 000111} is regular again.

  For super set  Not necessarily regular (take $\Phi$  is regular )

  So we can say  subset /superset of regular language need not be regular.

  Regular languages are not closed under the subset/superset relation.

Comments

I just try to learn as much as i can

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@shivani No Dfa will have 3 state .Since No  a will come after b.

nfa will have 2 state.

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yaaa yes @ManojK

Answer 3

1.L={A^mB^n   |m,n>=0}

2.NO.....FROM UR 1ST QUESTION a*b* (regular) a subset will be {a^nb^n  |n=>0 } not regular

3.         a^nb^n=non regular......and  a*b*=regular

Comments

in this a*b* i am confused only in one thing why don't we use n ,n  in place of * why to use n  m .it is not explicitly mention anywhere that you have to use n and m we are free to use either one.

in second ans as you said that a^b^n is a subset of a^n b^m i am confused here too .we are using n ,n as a subset of m ,n why? i always assume n  ,n should be greater .then n ,m

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1.a*b*={null,a,b,aaaaaa,bbbbb,abbb........} but a^nb^n={null,ab,aabb,aaabbb........}

so in a*b* if u take n inplace of * then  will miss some strings

2.. in second i m not saying a^nb^n is subset of a^nb^m im saying that FROM UR 1ST QUESTION a*b* (which is regular)  and its subset will be {a^nb^n \n>=0} which is not regular