Explanation Given: The set of all bit strings that contain three consecutive 1s. Calculation: We are interested in constructing a deterministic finite-state automation that recognized all bit strings S containing three consecutive 1s. Let the start state be s 0 . Let us consider four states s 0 , s 1 , s 2 , s 3 . s 1 will represent that the last digit was 1. s 2 will represent that that the last two digit were 11. s 3 will represent that the string contained 111. s 3 will all be final states, as we are interested in the strings containing three consecutive 1s. We move from s 0 to s 1 , if we come across a 1, else we remain at s 0 . We move from s 1 to s 2 , if there is a second 1, else we move back to s 0 . We move from s 2 to s 3 , if there is a third 1, else we move back to s 0 . Once we arrived at s 3 , because we will always know that the string contained a 111

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Chapter 13.3, Problem 29E

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Construct a deterministic finite-state automaton that recognizes the set of all bit strings that contain three consecutive 1s.

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Chapter 13.3, Problem 28E

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Construct a deterministic finite-state automaton that recognizes the set of all bit strings that contain three consecutive 1s.

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Construct a deterministic finite-state automaton that recognizes the set of all bit strings that contain three consecutive 1s.

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