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How would I design an NFA that accepts all strings don't end in a certain sequence over the alphabet {0,1}. Designing a DFA that does the job is fairly straight forward, but I can't find out how to make my Automata Non-Deterministic.

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Any DFA is also already a NFA, so you've already answered your question.

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Actually "non-deterministic automaton" is a horrible name. It better be "(finite) automaton" which has a subclass of "deterministic" automata. I do not think people are really interested in the construction of an automaton that is on purpose non-deterministic.

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    $\begingroup$ It's a pretty common convention in mathematics that the "non-" prefix doesn't mean "not" but rather "not necessarily". $\endgroup$ – Nate Eldredge Dec 10 '17 at 4:46

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