CS3452 Theory of Computation
IAT 1 Question Bank
PART – A
1. Prove 12 + 22 + 32 + ⋯ + 𝑛2 =
𝑛(𝑛+1)(2𝑛+1)
using mathematical induction.
6
Define ∈ −transition.
Define ∈ − closure of a state with an example.
Define Finite Automata. Give one example.
State pumping lemma for regular languages.
Let 𝐿 = {𝑤: 𝑤 ∈ {0,1}∗ 𝑤 𝑑𝑜𝑒𝑠 𝑛𝑜𝑡 𝑐𝑜𝑛𝑡𝑎𝑖𝑛 00 𝑎𝑛𝑑 𝑖𝑠 𝑛𝑜𝑛 𝑒𝑚𝑝𝑡𝑦}. Construct a regular expression that
generates L.
7. Prove that reversal of any regular language is also regular.
8. Write regular expression for the language L= {Set of strings with even number of 1’s followed by odd number
of 0’s}.
9. Write the Chomsky hierarchy of grammar.
10. Write CFG to accept the language defined by 𝐿 = {𝑎𝑖 𝑏 𝑗 𝑐 𝑘 : 𝑖, 𝑗, 𝑘 ≥ 0 𝑎𝑛𝑑 𝑖 = 𝑗 + 𝑘}.
11. Check whether grammar: E-> E +E | E*E| id is ambiguous.
12. Convert the CFL, 𝐿 = {𝑤|𝑤 = 𝑤 𝑅 , 𝑤 𝑖𝑠 𝑎 𝑝𝑎𝑙𝑖𝑛𝑑𝑟𝑜𝑚𝑒} to CFG.
2.
3.
4.
5.
6.
PART – B
1. Construct DFA equivalent to the following NFA. Consider 𝑀 = ({𝑝, 𝑞, 𝑟, 𝑠}, {0,1}, 𝛿, 𝑝, {𝑠}) where 𝛿 is
defined as
Input Symbol
State
0
1
{𝑞, 𝑠} {𝑞}
𝑝
{𝑟}
{𝑞, 𝑟}
𝑞
{𝑠}
{𝑝}
𝑟
--{𝑝}
𝑠
2. Prove that if a Language L is accepted by some 𝜖 − NFA if and only if L is accepted by some DFA.
3. Convert the following 𝜖- NFA to its equivalent DFA.
4. Convert the following 𝜖- NFA to its equivalent DFA.
5. Minimize the following DFA
6. Minimize the following DFA
7. Show that L = { a𝑛 𝑏𝑛 where n ≥ 1} is not regular.
8. Check whether the language 𝐿 = {𝑥 ∈ {𝑎, 𝑏}∗ | 𝑛𝑎 (𝑥) > 𝑛𝑏 (𝑥)} is regular or not.
9. Explain the any five closure properties of regular languages.
10. Construct a regular grammar for the following RE: 10 + (0 + 11)0*1
11. Construct an RE from the given FA using state elimination method.
12. Construct an RE from the given FA using state elimination method.
13. Construct an FA equivalent to the RE: L = (a + b)*(aa + bb)(a + b)*.
14. Explain about the Chomsky hierarchy of languages.
15. Examine whether the given grammar 𝐺 = ({𝐸}, {+, −, 𝑖𝑑}, {𝐸 → 𝐸 + 𝐸 , 𝐸 → 𝐸 − 𝐸 , 𝐸 → 𝑖𝑑}, {𝐸})
is ambiguous or not.
16. Identify a CFG to generate even set of palindrome over alphabet {a,b}. Choose a string from L and for the
derived string give
i) Left most derivation ii) Right most derivation iii) Derivation Trees.