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Non-deterministic FSA

Non-deterministic FSA. Regular Languages . A Language is called Regular iff there is a DFA acceptor that defines it. There exists some DFA M such that L = L(M). NFA. Two non-deterministic elements: Lambda transitions 2 outarcs with same symbol

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Non-deterministic FSA

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  1. Non-deterministic FSA

  2. Regular Languages A Language is called Regular iff there is a DFA acceptor that defines it. There exists some DFA M such that L = L(M).

  3. NFA • Two non-deterministic elements: • Lambda transitions • 2 outarcs with same symbol • A String is accepted if there is SOME path that ends in an acceptor state.

  4. Example {ab, abc}* q1 a q0 b c,λ q2

  5. Example Is aaa accepted? ab? a? abb? b? q1 a q0 b a λ q2

  6. Intuitive NFA’s • Example: Write a DFA & NFA that accept the strings containing the substring abbab

  7. Practice - write NFAs • Strings on {a,b}* that have exactly 2 a’s or more than 2 b’s. • A string on {a,b}* that starts and ends with “ab”.

  8. Things NFA’s make easy • Practice: • Prove if L is regular, LR is regular.

  9. Equivalence • DFA’s and NFA’s are equally powerful. • That is, For every language accepted by a NFA, there exists some DFA that also accepts the language.

  10. Equivalence - Proof by construction • Idea: Take every subset of states in DFA. Those are states in NFA. Make appropriate arcs. Any state with a final state in DFA becomes final in NFA.

  11. Example b a q2 qo q1 λ a

  12. b a q2 qo q1 λ a a q1orq2 qo b a

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