B.L.D.E.A’s V.P. Dr. P.G.H. College of Engineering &TechnologyDepartment of Computer Science and Engineering

Subject: FLAT Date: 03-08-2016 Subcode:10CS56 Staff Name: Laxmi Shabadi Sem : Vth ‘A’

NOTE: Last date for submission is on or before 25-08-2016

FLAT ASSIGNMENT QUESTIONS

UNIT 2

Q1. Convert the following ɛ-NFA into equivalent DFA

δ ɛ a b cp {p,q} Φ {q} {r}*q Φ {p} {r} {p,q}R Φ Φ Φ φ

Q2. Define regular expression and also write the regular expression for the following language

i) L={wɛ{a,b}*| w has exactly one pair of consecutive a’sii) Set of all strings not ending with the substring ‘ab’ over {a,b}

Q3. Define ɛ-NFA and ɛ-closure.

Q4. Construct the ɛ-NFA that accepts 01(0+1)*

Q5. Let R be a regular expression, then their exist a finite automata M=(Q, Ʃ,δ,q, F). Prove the above theorem

Q6. Give regular expression for the following language

i) L={w|w is in {a,b}* and |w|mod 3=0}ii) L={w|w is a string of even number of 0’s followed by odd number of

1’s}

Q7. Convert the regular expression (0+1)*1(0+1) to ɛ-NFA

Q8. Mention the applications of regular expression.

Q9. Giv ethe regular expression for the following language

i) L={anbm|n<=4, m>=2}ii) L={anbm|m+n is even}

Q10. Let M=(Q, Ʃ, δ, q, F) be a finite automata recognizing the language L. Then there exist an equivalent regular expression R for the regular language L such that L=L(R) {Kleene’s Theorem}

Q11. Obtain the regular expression for the following DFA using state elimination method

Q12. Consider the DFA show below

δ 0 1

q1 q2 q1

q2 q3 q1

*q3 q3 q2

Obtain the regular expression Rij and simplify the RE as much as possible.