Lecture2 Finite Automata - CS 172 Computability and...

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1 CS 172: Computability and Complexity DFAs and NFAs Sanjit A. Seshia EECS, UC Berkeley Acknowledgments: L.von Ahn, L. Blum, M. Blum S. A. Seshia 2 What we’ll do today Introduction to – DFA : Deterministic Finite Automata – NFA : Non-deterministic Finite Automata DFAs to/from regular languages Operations on regular languages Non-determinism and NFAs Pick up HW1 at the end of class!
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2 S. A. Seshia 3 0 0,1 0 0 1 1 1 start state q 0 transitions accept/final states, F states, Q DFA Terminology S. A. Seshia 4 0 0,1 0 0 1 1 1 q 3 q 0 q 1 q 2 M = (Q, Σ , δ , q 0 , F) What are 1.Q 2. F 3. Σ 4. δ
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3 S. A. Seshia 5 Acceptance (Formal Def.) M is a DFA with alphabet Σ An input string (word) w = w 1 w 2 w 3 … w n where each w i Σ ε denotes the empty string M accepts w if “after fully reading w it ends in an accept state” – If there is a sequence of states s 0 , s 1 , … s n such that • s 0 = q 0 • s i = δ (s i-1 , w i ) • s n F S. A. Seshia 6 Regular Language M is a DFA with alphabet Σ L(M) is the set of strings accepted by M – L(M) is the language of M – M recognizes L(M) Regular language: set of strings that is the language of some DFA The set of all possible strings is denoted Σ * • Is Σ * regular?
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4 S. A. Seshia 7 0,1 q 0 L(M) = ?
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