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NFA->DFA

NFA->DFA. COP4620 – Programming Language Translators Dr. Manuel E. Bermudez. NFA->DFA. Done. Soon. RG R RG L Minimum DFA RE NFA DFA. Now. Deterministic Finite-State Automata (DFA’s)

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NFA->DFA

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  1. NFA->DFA COP4620 – Programming Language Translators Dr. Manuel E. Bermudez

  2. NFA->DFA Done Soon RGR RGL Minimum DFA RE NFA DFA Now

  3. Deterministic Finite-State Automata (DFA’s) Definition: A deterministic FSA is defined just like an NFA, except that δ: Q x Σ → Q, rather than δ: Q x Σ U {ε}→ 2Q Thus, both and are impossible. For every NFA there exists an equivalent DFA (accepting the same language). NFA->DFA ε a a

  4. Conversion from NFA’s to DFA’s: Simulate NFA moves with the DFA. DFA start state: NFA start state S, and all ε-reachable states from S. Each DFA state: a subset of the set of NFA states. New DFA states: Calculate the states reachable through each t  Σ. Final DFA states: contain any NFA final state. NFA->DFA

  5. Input State a b 123 23 456 23 23 6 456 56 --- 6 --- --- 56 56 --- In general, if NFA has N states, The DFA can have as many as 2N states. a ε 2 3 b ε a 6 1 b ε ε 4 5 NFA->DFA NFA: DFA: a b 6 23 a 123 b a a 456 56

  6. State a b 0 --- 1 1 234689 --- 234689 34568910 346789 34568910 34568910 34678911 346789 34568910 346789 34678911 34568910 346789 ε NFA->DFA NFA: from ba(a+b)*ab a 4 5 ε ε ε a b b a ε 10 9 11 8 2 0 1 3 a ε 6 7 ε b 34568910 b a ε b a a 0 1 234689 a 34678911 b 346789 b DFA: b

  7. NFA->DFA Done Soon RGR RGL Minimum DFA RE NFA DFA Done

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