Lecture 3

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Proof (not effective!) If L is a regular language and S is an arbitrary set then L/S is regular Let M = (Q,Σ,δ,q0,F) be a DFA for L There is a DFA M’= (Q,Σ,δ,q0,F’) that accepts L/S M’ behaves just like M, but F’ consists of just those states for which ∃y∊S such that δ(q,y)∊F I don’t (and cannot in general) know what F’ is but I know it exists! Friday, February 8, 13
Proving language no regular In general this is harder! We need a property that all regular languages possess And a way to show that a language does not possess that property The property: “pumpability” Friday, February 8, 13
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Lecture 3

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