Examples for Finite Automata

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Examples for Finite Automata
Fall 2009

• CSC3130 Tutorial One

Xiao Linfu
lfxiao_at_cse.cuhk.edu.hk
Department of Computer Science Engineering
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Outline

• DFA example
• NFA example
• NFA to DFA conversion
• Regular Expressions

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DFA

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

x
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NFA

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

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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
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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.

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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
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NFA Example

• Construct NFAs for the following languages over
  the alphabet a, b, , z
• All strings that contain eat or sea or easy

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NFA Example

• Construct NFA for the language over the alphabet
  a, b, , z such that every string doesnt
  contain fool.

dead state
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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
• (acd)b(acd)

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Regular Expressions

• - Alphabet X 0, 1
• (0 1)
• the set of all binary strings
• 03104
• all strings consisting of three 0s, followed
  by any number of 1s, followed by four 0s
• 01001
• all strings starting with any number of
  0s, followed by 100, followed by and number of
  1s

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• Thank you!