Question Bank
Subject:-TOC
Q1. Prove the formula
a) (r * s*) = (r + s) *
Class:-TE Computer
b) (ab)* ≠ a* b*
Q2. Define NFA and DFA
Q3. b) Prove that the regular expression P and Q
P= (1+011)*
Q=ε+1*(011)*(1*(011)*)*
a) Prove that (1+00*1)+(1+00*1)(0+10*1)*(0+10*1)=0*1(0+10*1)*
Q4. Show that
b) i) R*R = R+
c) ii) (P + Q)* = (P*Q*)*
d) iii) (R*)* = R*
Q5. Find all strings of length 5 or less in the regular set represented by the
Following
i) (ab + a)* (aa + b)
ii) (a*b + b*a)*a
iii) a* + (ab + a)*
Q6. Design DFA that accept all string containing even number of zero’s and even
Number of one’s over ∑= {0, 1}.
Q7. Design a DFA for a language of strings of 0’s and 1’s such that
a) Substring is 10.
b) Strings ending with 101.
Q8. Define Mealy and Moore machine
Q9. Design an NFA to accept set of all strings which end with 00. Where I = {0, 1}.
Q10. The transition table of a NFA ‘M’ is given below. Construct a DFA equivalent to M. δ
is
Q0
Q1
Q2
Q3
Q4
0
q1q4
-
1
q4
q4
q4
-
2
q2q3
q2a3
-
Q11. Construct a Moore Machine equivalent to the Mealy Machine M given
Below δ is
Q1
Q2
Q3
Q4
a=0
Q1
Q4
Q2
Q3
1
1
1
0
a=1
Q2
Q4
Q3
Q1
0
1
1
1
Q12. Design a Mealy Machine to find out 2’s complement of a given binary number.
Q13. Give the Moore machine for the following processes. “For input from
(0 + 1)*, if inputs ends in 101, output X; if input ends in 110, output Y,
Otherwise output Z”
Q14. Design Mealy machine for incrementing the value of any binary number by one.
Q15. Find a regular expression corresponding to each of the following subsets of {0, 1}*.
a) The language of all strings containing exactly two 0’s.
b) The language of all strings containing at least two 0’s.
c) The language of all strings not containing the substring 00.
d) The language of all string starting with 0 and ending with 1.
Q16. Construct the DFA for following languages
a) L={x ε (a,b,c)*: x contains exactly one b immediately following c}
b) L={x ε (0,1)*: x is starting with 1 and |x| is divisible 3}
c) L={x ε (a,b)*:x contains any number of a’s followed by at least one b}
Q17 . Construct a DFA with reduced states equivalent to the regular expression
10 + (0+11)0*1.
Q18. Consider the following NFA with E-transitions. Convert this in to
1) NFA without ∈-moves
2) DFA
Q19. For the following regular expression, draw an FA recognizing the corresponding
language. r = (1+10)* 0
Q20. State Pumping Lemma for RL.
Q21. State Arden’s Theorem and prove it.
Q22. Draw TG for set of strings with odd length over alphabet {0,1} find its RE using Ardens
theorem.