Virtual Labs

What is the primary purpose of DFA minimization?

a: To make the DFA accept more strings Explanation

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b: To reduce the number of states while preserving the accepted language Explanation

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c: To convert the DFA to a different type of automaton Explanation

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d: To increase the speed of state transitions Explanation

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What types of states are removed first during DFA minimization?

a: Accepting states Explanation

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b: States with the most transitions Explanation

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c: Unreachable states Explanation

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d: States with self-loops Explanation

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In the initial partitioning step of DFA minimization, how are states grouped?

a: By the number of incoming transitions Explanation

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b: By their position in the state diagram Explanation

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c: Into accepting and non-accepting states Explanation

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d: Randomly into equal-sized groups Explanation

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Two states can be merged in DFA minimization if they:

a: Have the same state name Explanation

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b: Are both accepting or both non-accepting Explanation

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c: Have identical transition behavior for all input symbols Explanation

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d: Are connected by a transition Explanation

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What does it mean for two DFAs to be equivalent?

a: They have the same number of states Explanation

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b: They have identical state transition diagrams Explanation

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c: They accept exactly the same language Explanation

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d: They use the same alphabet Explanation

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In partition refinement, when must two states in the same partition be separated?

a: When they have different state names Explanation

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b: When they transition to states in different partitions on some input symbol Explanation

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c: When they have different numbers of outgoing transitions Explanation

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d: When they are not adjacent in the state diagram Explanation

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What is the time complexity of the standard DFA minimization algorithm?

a: O(n) where n is the number of states Explanation

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b: O(n log n) where n is the number of states Explanation

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c: O(kn²) where n is the number of states and k is the alphabet size Explanation

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d: O(2ⁿ) where n is the number of states Explanation

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Which property must be preserved during DFA minimization?

a: The exact state names Explanation

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b: The number of transitions Explanation

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c: The accepted language Explanation

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d: The visual layout of the state diagram Explanation

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How can you verify that two DFAs are equivalent?

a: Count their states and compare the numbers Explanation

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b: Check if they have the same start state name Explanation

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c: Minimize both DFAs and compare their structure Explanation

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d: Test them on a few sample strings Explanation

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DFA Minimization and Equivalence