# Module20 - Module 20 NFA's with-transitions NFA's Formal...

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1 Module 20 NFA’s with λ -transitions NFA- λ ’s Formal definition Simplifies construction LNFA- λ Showing LNFA is a subset of LNFA and therefore a subset of LFSA

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2 Defining NFA- λ ’s
3 Change: λ -transitions We now allow an NFA M to change state without reading input That is, we add the following categories of transitions to δ δ (q ,λ29 is allowed

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4 Example * a,b a a,b a b a b a,b a,b a a b λ λ
5 Defining L(M) and LNFA- λ M accepts string x if one of the configurations reached is an accepting configuration – (q 0 , x) |- * (f, λ ) where f in A M rejects string x if all configurations reached are either not halting configurations or are rejecting configurations L(M) or Y(M) N(M) LNFA- λ Language L is in language class LNFA- λ iff

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6 LNFA- λ subset LFSA Recap of what we already know Let M be any NFA – There exists an algorithm A 1 which constructs an FSA M’ such that L(M’) = L(M) New goal Let M be any NFA- λ – There exists an algorithm A 2 which constructs an FSA M’ such that L(M’) = L(M)
7 Visualization Goal Let M be any NFA- λ – There exists an algorithm A 2 which constructs an FSA M’ such that L(M’) = L(M) NFA- λ M FSA M’ A 2

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Module20 - Module 20 NFA's with-transitions NFA's Formal...

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