Minimization of DFA MCQs

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

What is the purpose of minimizing a DFA?

A) To reduce the number of input symbols.
B) To reduce the number of states.
C) To reduce the number of transitions.
D) To reduce the length of accepted strings.
Answer: B

Which of the following steps is part of the DFA minimization process?

A) Removing all states.
B) Combining equivalent states.
C) Adding new states.
D) Removing all transitions.
Answer: B

The first step in minimizing a DFA is to:

A) Identify unreachable states.
B) Identify dead states.
C) Combine equivalent states.
D) Construct the transition table.
Answer: A

During DFA minimization, states are considered equivalent if:

A) They have the same number of incoming transitions.
B) They have the same number of outgoing transitions.
C) They have identical transitions for all input symbols.
D) They cannot be distinguished by any string.
Answer: D

In the process of DFA minimization, a state is considered unreachable if:

A) There are no transitions leading to it.
B) It has no outgoing transitions.
C) It is not the start state.
D) It is not an accept state.
Answer: A

Which algorithm is commonly used for DFA minimization?

A) Dijkstra’s algorithm
B) Floyd-Warshall algorithm
C) Hopcroft’s algorithm
D) Kruskal’s algorithm
Answer: C

The minimization process of a DFA results in:

A) A DFA with the maximum number of states.
B) A DFA with a unique start state.
C) A DFA with the minimum number of states.
D) A DFA with a unique accept state.
Answer: C

In the minimization of a DFA, when two states are combined, it is important that they:

A) Have the same incoming transitions.
B) Have the same outgoing transitions.
C) Are both accept states or both non-accept states.
D) Are reachable from the start state.
Answer: C

After removing unreachable states in a DFA, what is the next step in the minimization process?

A) Removing dead states.
B) Combining equivalent states.
C) Constructing the transition table.
D) Adding new states.
Answer: B

Which of the following is a result of DFA minimization?

A) An NFA with fewer states.
B) A DFA with more transitions.
C) A minimized DFA that recognizes the same language.
D) A context-free grammar.
Answer: C

When two states are indistinguishable in a DFA, it means:

A) They accept different sets of strings.
B) They have different outgoing transitions.
C) They cannot be distinguished by any string.
D) They have the same incoming transitions.
Answer: C

The process of minimizing a DFA involves constructing a partition of states. This partition is initially:

A) Divided into reachable and unreachable states.
B) Divided into accept and non-accept states.
C) Divided based on incoming transitions.
D) Divided based on outgoing transitions.
Answer: B

Which of the following statements is true for a minimized DFA?

A) It has more states than the original DFA.
B) It recognizes a different language than the original DFA.
C) It has fewer transitions than the original DFA.
D) It has the same number of states as the original DFA.
Answer: C

In a minimized DFA, each state represents:

A) A single string.
B) A set of indistinguishable states.
C) A single input symbol.
D) A single transition.
Answer: B

During the DFA minimization process, a pair of states is repeatedly split until:

A) All states are reachable.
B) No further splits are possible.
C) All transitions are utilized.
D) All states are dead.
Answer: B

The table-filling method for DFA minimization is used to:

A) Identify unreachable states.
B) Identify and mark distinguishable pairs of states.
C) Combine equivalent states.
D) Add new transitions.
Answer: B

Which of the following is not affected by the DFA minimization process?

A) The number of states.
B) The language recognized by the DFA.
C) The number of transitions.
D) The alphabet of the DFA.
Answer: D

After minimizing a DFA, the resulting DFA is:

A) Guaranteed to have exactly one start state and one accept state.
B) Guaranteed to have the minimum number of states necessary to recognize the language.
C) Guaranteed to have no unreachable states.
D) Guaranteed to have the maximum number of states.
Answer: B

Which of the following best describes an equivalence class in the context of DFA minimization?

A) A set of states that are reachable from each other.
B) A set of states that have the same transitions for all input symbols.
C) A set of states that cannot be distinguished by any string.
D) A set of states that all have the same outgoing transitions.
Answer: C

A minimized DFA will have:

A) The same number of states as the original DFA.
B) Fewer or the same number of states as the original DFA.
C) More states than the original DFA.
D) Fewer transitions than the original DFA.
Answer: B

The final partition in the table-filling method represents:

A) The unreachable states.
B) The dead states.
C) The equivalence classes of the minimized DFA.
D) The initial states of the DFA.
Answer: C

 

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