Equivalence of DFA and NFA MCQs

By: Prof. Dr. Fazal Rehman Shamil | Last updated: September 23, 2024

Which of the following statements is true about the equivalence of DFA and NFA?

A) Every DFA has an equivalent NFA, but not every NFA has an equivalent DFA.
B) Every NFA has an equivalent DFA, but not every DFA has an equivalent NFA.
C) Every NFA has an equivalent DFA, and every DFA has an equivalent NFA.
D) DFA and NFA are not equivalent.
Answer: C) Every NFA has an equivalent DFA, and every DFA has an equivalent NFA.

Given an NFA with
š‘›
n states, the equivalent DFA will have at most:

A)
š‘›
n states
B)
2
š‘›
2
n
states
C)
š‘›
2
n
2
states
D)
š‘›
+
1
n+1 states
Answer: B)
2
š‘›
2
n
states

What is the primary difference between a DFA and an NFA?

A) A DFA can have epsilon transitions, while an NFA cannot.
B) An NFA can have multiple transitions for a single input from a given state, while a DFA cannot.
C) An NFA accepts different languages than a DFA.
D) A DFA can be converted to a Pushdown Automaton, while an NFA cannot.
Answer: B) An NFA can have multiple transitions for a single input from a given state, while a DFA cannot.

Which construction method is used to convert an NFA to an equivalent DFA?

A) Pumping Lemma
B) Myhill-Nerode Theorem
C) Subset Construction (also known as the Powerset Construction)
D) Chomsky Normal Form
Answer: C) Subset Construction (also known as the Powerset Construction)

In the context of DFAs and NFAs, what does it mean for two automata to be equivalent?

A) They have the same number of states.
B) They accept the same language.
C) They have the same transition function.
D) They are in the same class of Chomsky hierarchy.
Answer: B) They accept the same language.

Which of the following is not true about converting an NFA to a DFA?

A) The start state of the DFA is the epsilon-closure of the start state of the NFA.
B) Each state in the DFA represents a set of states in the NFA.
C) The DFA may have more states than the NFA.
D) The resulting DFA always has fewer states than the NFA.
Answer: D) The resulting DFA always has fewer states than the NFA.

How does nondeterminism in an NFA affect its ability to recognize languages compared to a DFA?

A) It allows the NFA to recognize a broader class of languages.
B) It allows the NFA to recognize only a subset of regular languages.
C) It does not affect the class of languages the NFA can recognize.
D) It restricts the NFA to only recognize finite languages.
Answer: C) It does not affect the class of languages the NFA can recognize.

When converting an NFA to a DFA, what does each state in the resulting DFA represent?

A) A single state in the NFA
B) A subset of states in the NFA
C) A transition in the NFA
D) An input symbol in the NFA
Answer: B) A subset of states in the NFA

True or False: Every DFA can be simulated by an NFA.

A) True
B) False
Answer: A) True

Which of the following is an advantage of using an NFA over a DFA?

A) NFAs are faster in processing input strings.
B) NFAs can recognize a wider range of languages.
C) NFAs can be more concise and have fewer states for certain languages.
D) NFAs are easier to implement in hardware.
Answer: C) NFAs can be more concise and have fewer states for certain languages.