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NFA, DFA, and regular expressions - 204213 Theory of Computation

NFA, DFA, and regular expressions - 204213 Theory of Computation

NFA, DFA, and regular expressions - 204213 Theory of Computation

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Outline Review Nondeterminism Eq. <strong>of</strong> <strong>NFA</strong>s <strong>and</strong> <strong>DFA</strong>s Closure Reg.Ex. Eq. between Reg.Ex. <strong>and</strong> FAaPro<strong>of</strong> by Structural InductionIn proving Lemma 5, we show how to construct an <strong>NFA</strong> <strong>of</strong> a<strong>regular</strong> expression given <strong>NFA</strong>s <strong>of</strong> its sub<strong>expressions</strong>.The pro<strong>of</strong> is again an inductive pro<strong>of</strong>.Sometimes, this kind <strong>of</strong> inductive pro<strong>of</strong>s is called structuralinduction.Inductive Hypothesis (when considering a <strong>regular</strong> expressionR): Assume that for all smaller <strong>regular</strong> <strong>expressions</strong> R ′ , thelanguage described by R ′ can be recognized by some <strong>NFA</strong> N ′ .

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