Lecture 10.pptx - Automata Theory Lecture 10 Recap Removing...

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Automata Theory Lecture 10
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Recap Removing Nondeterminism from NFA because of multiple edges NFA-^ to NFA to FA Kleene’s theorem – Part 1 – RL to FA Two ways to construct FA
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Kleene’s theorem – Part 2 Statement If M is FA then L(M) is regular language
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Proof Important points States in Q are numbered from 1 to n where n is total number of states. L(p, q, j) = Is a set of strings causing to move from p to q without going through a state numbered higher than j. Basic step: L(p, q, 0) is regular and covers and ^. Induction hypothesis: Assume L(p, q, k) is regular and prove L(p, q, k+1) is regular too.
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Proof To prove L(p, q, k+1) is regular there are two possibilities.
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