Prove that if two states of a finite-state automaton are k-equivalent for some integer k, then those states are m-equivalent for every nonnegative integer .
That equivalent two state of a finite-state automaton are equivalent for every nonnegative integer .
the constants and are nonnegative integers.
Let be a finite-state automaton which has and as equivalent states. The next-state function is considered as .
When we assign an input string which is the length of is less than or equal for the states and , then both states and are accepting or both states are nonaccepting
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