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Assignment 2

The document outlines an assignment with various tasks related to regular expressions and finite automata, including proofs, constructions, and identities. It covers topics such as proving non-regular languages, constructing equivalent finite automata, and deriving regular expressions. The submission date for the assignment is set for May 29, 2024.

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29 views2 pages

Assignment 2

The document outlines an assignment with various tasks related to regular expressions and finite automata, including proofs, constructions, and identities. It covers topics such as proving non-regular languages, constructing equivalent finite automata, and deriving regular expressions. The submission date for the assignment is set for May 29, 2024.

Uploaded by

Mir
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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ASSIGNMENT 2

SUBMISSION DATE :- 29/05/2024


1.Prove :

i) R=(1+00*1) + (1+00*1) (0+10*1)* (0+10*1)* = 0*1(0+10*1)*

ii) R= Є+1* (011)* (1* (011)* ) *= (1+011)*

2. a) List out the identities of Regular expression.

b) From the identities of RE, prove that

i) 10+(1010)*[^+(1010)*]=10+(1010)*

ii)(0+011*)+(0+011*)(01+0100*)(01+0100*)*=01*(010*)*

3. a) Construct an equivalent FA for the given regular expression (0+1)*(00+11)(0+1)*

b) State Arden’s theorem and construct the regular expression for the following FA using Arden’s
theorem.

c) Construct a finite automata forthe regular expression R = (0 + 1(01)*)*

4. a) Prove that the language L= {an b n c n | n>=1} is not regular using pumping lemma.

b) Prove that L = {ww | w ∈ {0, 1}* } is not regular.

5. Write Regular expression for the following L = { an bm : m, n are even} L = { an ,bm : m>=2, n>=2}

6. Prove that L={w|w is a palindrome on {a,b}*} is not regular. i.e., L={aabaa, aba, abbbba,…}

8. Prove that L={ all strings of 1’s whose length is prime} is not regular. i.e., L={12,13 ,15 ,17 ,111 ,----}

9. Obtain a regular expression for the FA shown below:

10.a) Show that P*(QP*)*= (P + Q)


b) Prove that E+ 1*(011)‘(1*(011)*)*= (1 +011)*

c) Prove that (1 +00*1) + (1 +00*1) (0+ 10*l)*(0+ 10*1) =0*1(0+ 10*1)*

d) Prove or disprove the given regular expression (rs + r)*= r(sr + r)*

11.a) Construct an NFA to accept the language represented by a*b*c*. Convert the NFA to its
equivalent DFA.

b) Construct an NFA with epsilon transition for the following RE:

(00 + 11)* (10)*

12. a)

b)

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