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# Quiz1-Sol - state B from state A and then consume the last...

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COT 4210 Quiz #1 Solutions 9/1/2011 1. Give the formal definition of the DFA drawn below. Answer Q = { X, Y, Z} Σ = {a, b} q 0 = X F = {Y} δ a b X Y Z Y Z X Z Z Y 2. Draw a DFA that accepts strings over the alphabet {0, 1} that start with 00 or end with 11. (Thus, 0010101 and 01010011 are in the language, but 010001 is not.) Answer

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The key here is that A, B and C keep track of strings that start with 00. E keeps track of strings that didn’t start with 00 that currently end in a 1. D keeps track of strings that didn’t start with 00 that currently end in a 0, while F keeps track of strings that didn’t start with 00 that currently end in 11. 3. Draw an NFA that accepts strings over the alphabet {1, b} that have a as their fourth letter from the end. (Thus, abbb and bbabaa are in the language while aba and bbabaaa are not.) Answer In this NFA, when we arrive at the fourth to last character, if it’s an a, we can guess and move to
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Unformatted text preview: state B from state A, and then consume the last three characters to end up at E. If the we don’t jump from state A to B on the fourth to last character, we can’t be accepted, and that jump can only occur if this character is an a, due to the transitions. 4. If an NFA has 20 states, what is the most number of states the corresponding equivalent DFA can have? Answer In the corresponding DFA, each state represents a subset of states from the NFA. Thus, the desired number is the maximum possible number of subsets of 20 items, which is 2 20 . Since the “null” state which corresponds to no possible output states doesn’t need to be drawn in most cases, 2 20 – 1, will also be accepted....
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Quiz1-Sol - state B from state A and then consume the last...

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