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(b) (30 points) Recall from the midterm that a symmetric NFA is just like an NFA except that for every q, q, E Q and
(b) (30 points) Recall from the midterm that a symmetric NFA is just like an NFA except that for every q, q, E Q and c E , if q, E (q, c) then we have that q E (q, c). That is, if there is a transition from q to q on character c then there is also one in the reverse direction on c. We draw this using an NFA diagram where all edges are undirected. We say that a language is symmetric regular if there exists a SNFA recognizing it. Define Sym to be the set of all languages decidable by a symmetric NFA. Show that Hint: to show a bijection exists between two sets A and B, it suffices to show that there is an injection from A to B and another injection from B to A. (b) (30 points) Recall from the midterm that a symmetric NFA is just like an NFA except that for every q, q, E Q and c E , if q, E (q, c) then we have that q E (q, c). That is, if there is a transition from q to q on character c then there is also one in the reverse direction on c. We draw this using an NFA diagram where all edges are undirected. We say that a language is symmetric regular if there exists a SNFA recognizing it. Define Sym to be the set of all languages decidable by a symmetric NFA. Show that Hint: to show a bijection exists between two sets A and B, it suffices to show that there is an injection from A to B and another injection from B to A
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