(10 points) We know that DFAS and NFAs are equivalent in power, but are they equivalent...

 

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(10 points) We know that DFAS and NFAs are equivalent in power, but are they equivalent in representational efficiency? Let L3 = {x|x is a binary string with a 1 as the 3rd character from the end}. Some examples of strings in L3 are 00100, 111, 100. Some strings not in L3 would be , 001, and 1011. Give a minimal DFA for L3 and a minimal NFA for L3. A minimal finite automaton for a language is the finite automaton with the fewest number of states that recognizes that language. Your minimal DFA should contain 8 = 23 states and your minimal NFA should contain 4 = 3+1 states. 1 (5 points) Give an NFA for the finite language L = { cat, dog, bird }. The procedure that you follow when producing this NFA should give you intuition for why every finite language is regular. (10 points) We know that DFAS and NFAs are equivalent in power, but are they equivalent in representational efficiency? Let L3 = {x|x is a binary string with a 1 as the 3rd character from the end}. Some examples of strings in L3 are 00100, 111, 100. Some strings not in L3 would be , 001, and 1011. Give a minimal DFA for L3 and a minimal NFA for L3. A minimal finite automaton for a language is the finite automaton with the fewest number of states that recognizes that language. Your minimal DFA should contain 8 = 23 states and your minimal NFA should contain 4 = 3+1 states. 1 (5 points) Give an NFA for the finite language L = { cat, dog, bird }. The procedure that you follow when producing this NFA should give you intuition for why every finite language is regular.