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Examples for Finite Automata

Learn about DFA, NFA, regular expressions, conversion techniques, and construction of DFAs for specific language patterns. Explore common prefix/suffix strings and practical examples with detailed explanations.

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Examples for Finite Automata

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  1. Fall 2009 Examples for Finite Automata Xiao Linfu CSC3130 Tutorial One lfxiao@cse.cuhk.edu.hk Department of Computer Science & Engineering

  2. Outline • DFA example • NFA example • NFA to DFA conversion • Regular Expressions

  3. DFA • For every string x, there is a uniquepath from initial state and associated with x. • x is accepted if and only if this path ends at a accept state. x

  4. NFA • For any string x, there may exist none or morethan onepath from initial state and associated with x. • x is accepted if there is some path that ends at a accept state.

  5. 0,1 1 0 1 q0 q1 q2 q3 start 0 1 0 q4 0,1 Strings With Common Prefix • Construct a DFA that accepts a language L over  = {0, 1} such that L is the set of all strings starting with “101”. absorbing state dead state

  6. 0 0 0 1 q0 q1 q10 q101 start 1 0 1 1 Strings With Common Suffix • Construct a DFA that accepts a language L over  = {0, 1} such that L is the set of all strings ending with “101”.

  7. 1,0 1 0 1 start q0 0 q1 q2 q3 0 0 1 1 q0 q0q1 q0q2 q0q1q3 start 1 0 1 NFA for Common Suffix • We can have a simpler representation for common suffix language using NFA: • Use subset construction to convert it to a DFA. compare with previous DFA

  8. all all e a t start q0 q1 q2 q3 s y q4 s e a q5 q6 NFA Example • Construct NFAs for the following languages over the alphabet {a, b, …, z}: • All strings that contain eatorseaoreasy

  9. ‘f’ not ‘f’ ‘f’ ‘f’ ‘f’ ‘o’ ‘l’ start q0 q1 q2 q3 q2 ‘o’ not ‘f’,‘o’ not ‘f’,‘l’ not ‘f’,‘o’ NFA Example • Construct NFA for the language over the alphabet {a, b, …, z} such that every string doesn’t contain “fool”. deadstate

  10. Regular Expressions - Alphabet X = {a, b, c, d} • (a + b)* all strings containing only a and b • c(a + b + c)*c2 all strings containing only a, b, and c that begin with c and end with cc 3) all strings containing only one b (a+c+d)*b(a+c+d)*

  11. Regular Expressions - Alphabet X = {0, 1} • (0 + 1)* the set of all binary strings • 031*04 all strings consisting of three 0’s, followed by any number of 1’s, followed by four 0’s • 0*1001* all strings starting with any number of 0’s, followed by 100, followed by and number of 1’s

  12. Thank you!

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