Question: 1. Let S = {a,b,c} and consider the language = {w 2* | w has length at least three and the third-to-last and second-to-last symbols

1. Let S = {a,b,c} and consider the language = {w

2* | w has length at least three and the third-to-last and

second-to-last symbols in w are different}. 3. Finally, give a much simpler

1. Let S = {a,b,c} and consider the language = {w 2* | w has length at least three and the third-to-last and second-to-last symbols in w are different}. 3. Finally, give a much simpler nondeterministic finite automaton whose language is the language defined in the previous question and explain (somewhat informally, and reasonably briefly) your answer is correct. Hint: One of the examples of a nondeterministic finite automaton discussed in the lec- tures on NFA's should be studied. You should find that that there is a nondeterministic finite automaton with only six states that has language . However, you will receive full marks if you give a correct NFA for this language with more states than that and explain why your answer is correct

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