1. DFA N = (Q_N, Σ, δ_N, s_N, F_N) where Q_N = ___ 2. DFA N = (Q_N, Σ, δ_N, s_N, F_N) where δ_N = ___ 3. DFA N = (Q_N, Σ, δ_N, s_N, F_N) where s_N = ___ 4. DFA N = (Q_N, Σ, δ_N, s_N, F_N) where F_N = ___ 5. DFA N = (Q_N, Σ, δ_N, s_N, F_N) where N accepts x if and only if ___
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The reverse of a string x, denoted rev(x), is the string obtained by writing x backwards. For example, if x = abbaaab then rev(x) = baaabba. If A is a subset of Σ*, the reverse of A, denoted rev(A), is the subset of Σ* consisting of all reverses of strings in A:
rev(A)={rev(x) | x∈A}
For example, rev({a,ab,aab}) = {a,ba,baa}. Suppose you are given a deterministic finite automaton M accepting a set A. Show how to construct a DFA N accepting rev(A). (Kozen would suggest putting pebbles on the final states of M and moving them backwards along transition edges.) Describe N formally (i.e. in terms of Q, δ, etc.) including the definition of acceptance. Hint: the subset construction will be helpful here. You can start with M = (Q, Σ, δ, s, F) and define the components of N in terms of the components of M.
1. DFA N = (Q_N, Σ, δ_N, s_N, F_N) where
Q_N = ___
2. DFA N = (Q_N, Σ, δ_N, s_N, F_N) where
δ_N = ___
3. DFA N = (Q_N, Σ, δ_N, s_N, F_N) where
s_N = ___
4. DFA N = (Q_N, Σ, δ_N, s_N, F_N) where
F_N = ___
5. DFA N = (Q_N, Σ, δ_N, s_N, F_N) where N accepts x if and only if ___
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