Topics include regular and context-free languages, decidable and undecidable problems, reducibility, recursive function theory, time and space measures on computation, completeness, hierarchy theorems, inherently complex problems, oracles, probabilistic computation, and interactive proof systems.
1. The password to the admins account=”administrator”. The total number of states required
to make a password-pass system using DFA would be __________
a) 14 states
b) 13 states
c) 12 states
d) A password pass system cannot be created using DFA
Answer: a
Explanation: For a string of n characters with no repetitive substrings, the number of
states required to pass the string is n+1.
2. Which of the following is the corresponding Language to the given DFA?
a) L = {x ϵ {0, 1} * | x ends in 1 and does not contain substring 01}
b) L = {x ϵ {0,1} * |x ends in 1 and does not contain substring 00}
c) L = {x ϵ {0,1} |x ends in 1 and does not contain substring 00}
d) L = {x ϵ {0,1} * |x ends in 1 and does not contain substring 11}
Answer: b
Explanation: The Language can be anonymously checked and thus the answer can be
predicted. The language needs to be accepted by the automata (acceptance state) in
order to prove its regularity.
, 3. Let ∑= {a, b, …. z} and A = {Hello, World}, B= {Input, Output}, then (A*∩B) U (B*∩A) can
be represented as:
a) {Hello, World, Input, Output, ε}
b) {Hello, World, ε}
c) {Input, Output, ε}
d) {}
Answer: d
Explanation: Union operation creates the universal set by combining all the elements of
first and second set while intersection operation creates a set of common elements of the
4. Let the given DFA consist of x states. Find x-y such that y is the number of states on
minimization of DFA?
a) 3
b) 2
c) 1
d) 4
Answer: b
Explanation: Use the equivalence theorem or Myphill Nerode theorem to minimize the
DFA.
5. For a machine to surpass all the letters of alphabet excluding vowels, how many number
of states in DFA would be required?
a) 3
b) 2
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