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DFA minimisation partitions the states by

  • A.merging all accepting states into a single final state
  • B.deleting the states that were unreachable in the original NFA
  • C.grouping states that cannot be distinguished by any input string
  • D.removing every state that has more than one outgoing transition

Answer: C

Correct answer: grouping states that cannot be distinguished by any input string

Two states are equivalent when no input string leads from one to acceptance and from the other to rejection, so nothing outside can tell them apart. Minimisation refines a partition until each block contains only mutually indistinguishable states and then collapses each block to a single state. Accepting and non-accepting states are distinguishable by the empty string and never merge.

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